In my RTOEE game I let one of the players have the Dwarven Axe as a martial proficiency. He wanted it for the theme of his dwarven fighter, and I didn't see any real big todoo about letting him have it. Plus I had just smeared his sorceror in one shot.
It's been about 10 months of gaming since then and the dwarf fighter has done well through the levels. He's been accompanied by a dual wielding human fighter the entire time and both are equally nasty. The dwarf does more damage per blow, but the human gets an extra blow in there every round.
I can see the arguements against this, as it's a free feat (and it is) but I can honestly say that it has not caused anyone in my group to bat an eyelash.
So, for what it's worth, go ahead and let it happen in your game if it makes you and your player happy. That's what is important. I have seen nothing to imply that I have destroyed my game beyond all utility. None of the players have negative responses to it in my game, and none of their characters seem weaker for it.
If it's better for your game to say 'no', do it and move along. Rules say that this weapon should remain outside the standard list of weapons. If you want to rule 0 it, go for it, if not, don't worry about it.