I'm not sure how much authority Didio has with larger media stuff, so I'd imagine that someone at WB had to, at the very least, approve of the idea and the pitch and facilitate between DC and Netherrealm.
Interactions between companies and company holdings involving the sharing of an IP is one of the things where my business education is sorely lacking; I focus on small business stuff and this is a level of "corporate" I only have a passing familiarity with.
But I actually think Netherrealm was a good fit for DC; Mortal Kombat is far more "out there" than other fighting games like Street Fighter or Tekken. I mean, you've got aliens, magic, alternate realities (or whatever the realms are), cyborg ninjas......it's much more high concept than its peers, and that's rather fitting for DC. Hell, it's not hard to imagine that the MK universe exists in DC's multiverse somewhere, and playing characters like Sub-Zero, you'd almost think they were actual DC characters if you didn't know any better. Of course, I say the same thing about Hellboy.....but I think DC should try to buy that entire property from Mignolia anyway.
Of course, the ultra-violence that Mortal Kombat made its name with, is well beyond the scope of DC's roster, but the studio respected that; I haven't seen Injustice Superman rip anyone's spine out of their mouth for example.
I dunno, I'm still waiting for a uber-immersive superhero RPG, like Skyrim but with capes. One that game happens.....I don't think I'll ever have to buy another video game again.