There was more than one person, myself included, who posted responses along the lines of "This might be permissible, and doesn't sound too unbalancing." I think we just got swamped.
I honestly don't understand why people feel the need to post when they aren't saying anything new. It just makes it harder to develop whatever idea has been proposed. If you want to have an argument, why not do it privately so that other voices can be heard?
Anyway, I too would like to see the character in question. There are plenty of ways to give a character +1 BAB without being unbalancing. Simply insisting on "the rules say this" is not productive, is not interesting, and doesn't help those who are intrigued by the situation and would like to hash it out.
The question is not, "Should this be allowed?", because D&D is designed to be open-ended. There are several examples of spells and magic which break rules (for example, the Hammer of Thunderbolts allows enhancement bonuses on strength to stack) while leaving vague the exact mechanisms by which these rules are broken. This is what the DM is for, and just because the DM allows an exception to occur doesn't mean that they're stretching the rules of the game beyond the breaking point.
The appropriate question is "What should this cost the player?" Let's think of creative ways to give the player what they want, and then let the player decide whether the price is worth it. Isn't this more fun to discuss?
For example:
1) Allow a wish to do it. The price is 5000xp.
2) Allow a wish to swap a mage level with a fighter level. The price is 5000xp plus the reduction in magical power.
3) Allow a wish to do it, but make the player aware that this is beyond the normal scope of a wish and there may be unforseen consequences. The price is 5000xp plus whatever the DM sees fit to impose, but the player doesn't know beforehand what the Monkey's Paw will be.
4) The wish will create some lesser version of Tenser's Transformation and make it permanent. Cost is 5000xp, plus more xp for the permanency effect. In addition, the BAB might be dispelled in the future.
5) Allow the character to level up in their humanoid "monster class", if they are a monster or wish to become one.
6) Allow the character to invest an entire level's worth of XP in gaining +1 BAB but no other special abilities.
Some of you may think that all of these options are unbalancing and shouldn't be allowed. If so, I hope you will keep it to yourself in the interests of cultivating a more interesting discussion.
So let's see that character, and let's see some other ideas!
--Ben