I don't think that it is mentioned in the rulebook, unless someone quotes the rulebook, or show us an official ruling?I thought he did quote the rule book.
This is in the FFG version of the rule book. Page 7 under the Results of Battle section, third paragraph in that section:
If both players mutually destroy each other in the hex, then the attacker wins and the defender loses.
I am guessing you might have the older WOC Avalon Hill version. It doesn't say so explicitly, but does say:
You win a battle if you attack on your turn and eliminate all the defenders's units in a space.
And then WOC clarified that further as Sphere already mentioned. Obviously, they made sure it was clear in the new version by FFG.