In 5th edition, 13C1: “it is considered fallen only when either player points this out.”; and 16E: “The flag is considered down when either player points this out.”
So the flag wouldn’t be considered fallen when White made his claim.
I must agree with Mr. Mulford here. Saying flag fall takes precedence allows basically
the possibility for a player to make a non-move, and then to punch the clock with the
deliberate thought of running his opponent out of time. I believe the rule book must be
taken in context, and interpreted as a whole. For example, a pawn promotion move is
not complete until the new piece replaces the pawn. To interpret the above incident
differently would be to interpret out of context with other rules.
Rob Jones
To answer your last question first:
I wouldn’t penalize white for lack of sportsmanship unless there were clear evidence that his error was deliberate.
And now for the rest:
You don’t say whether this was a sudden death situation, but I’m going to assume it was.
I’m not sure why you think Rule 16R is relevant. Rule 16R is specifically addressing the situation in which an illegal move isn’t recognized until a number of moves (not exceeding 10) have been made, and the conclusion is that “the position before the illegal move is reinstated” but “the players do not recover the time they used after the illegal move.”
But (assuming this is sudden death) then the relevant rule is 11D, which states that “two minutes shall be added to the remaining time of the opponent of the player who made the illegal move.” Note that this rule specifically restricts itself to the situation in which “a player completes an illegal move by pressing the clock”. A player who makes an illegal move but recognizes the error and corrects it before pressing the clock is subject only to the limitations imposed by the touch-move rule (10B). The rationale for this, I gather, is that the player who presses the clock before correcting the error has deprived his opponent of an undeterminable amount of time (i.e., the time between the pressing of the clock and the moment when his opponent pauses the clock to make a claim), and that therefore his opponent should have extra time added to his clock to compensate for this.
The only question, then, is whether this extra time should be added, even if the opponent’s flag fell before he could pause the clock.
The problem with this is that the game is still in progress until a claim is made under Rule 13C. Of course, technically Rule 11D1 only applies in cases where the TD observes an illegal move which is not corrected. In this case, white is making a claim in an attempt to have the move corrected. I gather from the wording of the original question that both white and black are making claims at the same time.
My ruling would be that white should have an extra two minutes added to his time, which would have the effect of reversing the flag fall. My reasoning is that to disallow the awarding of extra time under Rule 11D in cases where the player’s flag has fallen would undermine the rationale for awarding extra time, since it would effectively negate the award in precisely those situations in which the award would be most likely to affect the outcome of the game.
True. But the rationale for the two minute award in Rule 11D, as I understand it, is that it is impossible to determine exactly how much time pressing of the clock after the illegal move cost the opponent of the player who made the error, and that therefore the award should err in the direction of favoring the errant player’s opponent. You can argue that white should not be rewarded for the fact that black made an inadvertent error, but I would argue that black should have been careful enough not to make the error in the first place. And if white is awarded an extra two minutes, black is likely to be more careful when he encounters similar situations in the future.
Well, Bob, you are writing your own version of the rulebook if you rule this way. 
I would treat it like any other illegal move: Black is bound by the touch-move rule, but can move the queen to any legal square.
Bob
Fair enough. I’ve used 1C2 on a few responses to the Senior TD test and the reasoning has been rejected by the TDCC. So I am very wary of paths that end up at 1C2 without ruling on the claims presented.
Luis probably has the experience to be an NTD. I was hopeful that he was granted that title when you mentioned it. I learned a ton from him while in Dallas.
As for his quote, “first” is the player who made his claim first. So if Black claimed the time win and then White said, “Hey wait a minute I’m claiming an illegal move!” then the TD would rule on the time claim first. Taken this way, a TD may never get to the illegal/non-move debate.
My unsolicited and overpriced $0.02:
In Mr. Jones’s hypothetical, Black has not yet made any move, legal or illegal. So, I would try to reset the situation to the last legal position, and reset the clock accordingly.
The question of whether/how I would adjust White’s clock is interesting. Given the parameters of Mr. Jones’s hypothetical, I would probably give White some extra time. My instinct says that 15-30 seconds should be enough to compensate White for the distraction without unduly influencing the progression of the game.
(Fair warning: I don’t have my rulebook with me, so I’ll probably fall back on ye olde director discretion to justify the unusual time addition. My goal would be to restore the game, as closely as possible, to what it was before Black played his non-move and pressed the clock.)
As long as we are talking hypotheticals, how about somebody not in time trouble staring at the imminent loss of a piece and trying to figure out how to get the most out of the resulting bad position. The opponent goes to watch other boards while waiting for a move. While engrossed in analysis the clock is hit starting the opponent’s time even though no move is made on the board. They opponent can see from some distance that no move has yet been made so does not return to play. Can the player who has not yet moved make a valid time claim when the time runs out?
A mighty odd hypothetical – that one can see all the pieces on the board but not the clock.
This is getting fun now 
Rob Jones
A clock with a rocker arm may be a bit difficult to discern. Seeing that the king is still in check may be easy even from a distance.
My answer: of course not, which is why the tournament director should adjust the clocks when a player (or a spectator) has improperly pressed the clock, at least in cases where it makes a significant difference such as when a player’s time has run out after an improper clock press.
I’m not a great fan of the black-letter wording in the rule book that (apparently) leaves the only recourse for a player whose opponent leaves the board in an unusable situation (not finishing a promotion or knocking pieces) is to put the clock back on the opponent. That works fine if the offender is short on time and the “victim” isn’t, but seems completely wrong if the situation is the reverse (as in this case).
I’ve relied on rule 1C2b to address this, but a better solution would be to change the rules to say that the director can adjust the clocks to restore time lost by the opponent in these situations, or in other cases where the clock is improperly pressed, e.g. Jeff’s example where the clock is pressed when the player hasn’t made a move. Blitz rule 9 includes a sentence which perhaps should also be in the main rule: “If the player presses the clock after displacing pieces, then a penalty may be assessed.”
By the way, I found a curious omission in rule 11D1.
What happens if a player makes an illegal move, the opponent doesn’t call it, and the opponent’s flag falls? Rule 11D1 doesn’t say. Blitz rule 7e says “An illegal move doesn’t negate a player’s right to claim on time, provided it is done prior to the opponent’s claim of an illegal move. If the claims are simultaneous, the player who made the illegal move loses.” There doesn’t appear to be a corresponding rule in the regular rules.
Going back to the question in the original post:
I would absolutely, without a doubt, disallow the time forfeit claim. Regardless of what any rule says, it is completely unfair to let a player time-forfeit because his opponent pressed the clock before making a proper move.
I would also add extra time to the player’s clock. Anywhere from 15 seconds to 2 minutes, depending on my mood.
Bill Smythe
Lots of work to be done on the rule if any changse are tee’d up. For instance…Rob Jones’s OP involved an attempted move. Some say it’s illegal, others say it’s a non-move. Jeff’s hypothetical involves no move at all and is much more clearly an improper clock press. Lots of slicing to be done.
That omission is mentioned in my post #282394. I didn’t mention it afterwards as we disagreed on whether the situation involved an illegal move. It appears that 11D1 would allow the TD to rule in favor of an illegal move claim over a time claim.
It’s all situational but the flagged player has to indicate a claim or objection somehow. I would probably allow it even after the flag if the player had a “what the h.ell?!?” look on his face as he tries to interpret the illegal move.
Amen!!! And thank you!! There should never be benefits of improper conduct.
Rob Jones