Alice is not "lying".

If by this you mean "Alice would explode at being called a liar," then I agree.

You cannot reduce human communication in these circumstances to the explicit meaning of words.

Communication is the transfer of information from speaker to listener: while I cannot reduce intent to the explicit meaning of words in this case I can reduce actual transfer to the explicit meaning of words (and a bit extra). The man in question is likely to be literal-minded, otherwise he would have picked up on the hint. (Men tend to be more literal than women.) Alice is the one who has an easier path to avoid communication breakdown.

she may not want to get into a fight about when they talk about it

They are in a fight about when they talk about it, and she is the one that elevated it from discussion to fight.

she may want Bob to figure it out for himself

This habit is not conducive to relationship success.