I'm not taking sides in this, mainly because I've not played DotA, but I've got these views:
I don't think Valve are in the wrong. That name was floating about and they took it. Warcraft 3 came out forever ago, and Blizzard (And the various communities around DotA) have had years to pick up the name legally. If any publisher/studio could put time and money into it, it's Valve. Look at Portal - That started life as an indie project and thanks to Valve, it became a cult hit. Look at CS - That started as a mod, and has grown into one of the most successful FPS games of all time, again, thanks to Valve.
But in a way I can see Blizzard's point. It's something strongly associated with Blizzard, even if just for the fact it was created within a Blizzard game. However, if they were as "about the community" as they say, then they would do more than kick up a hissy fit about it.
Basically, I have to side with the "Blizzard are pissy because Valve got it" people. But I believe that Valve could pull this off, and I wouldn't trust Blizzard to do it at all. They're too busy with WoW, SC2, Diablo 3, probably a bunch of other projects and filling Kotick's coffers.