THere should be no DOG on this play. If the BJ whistles it dead as he should, the runner will stop. If the BJ doesn't blow it dead, then it's on the BJ and not on the runner. The only time you should ever have a DOG after a FC signal is if the runner just plain refuses to stop after the whistle is blown. If he starts to run, just blow it dead and keep the flag in your pocket.
I agree... and honestly, I'd probably say that there probably shouldn't be an invalid fair catch signal either, unless there was clearly intent to deceive.
If R11 changes his mind mid signal and wants to run instead of fair catch, too bad -- he gave a signal, it's a fair catch, ball is dead. His post catch run shouldn't be DOG unless he goes 90 yards for a "touchdown" despite a chorus of whistles in his ear.
However, if we have three flags on the ground and we're enforcing three penalties, I stand by my earlier comment.