I'm certain I don't understand the entirety of ODNS - but the basics still have to exist - something still needs to make a query on behalf of the initial user to some authoritative server (unless the answer is already cached). I guess, what I'm picturing in this case, is that if the trusted resource (ODNS Stub) exists in your local infrastructure, then the source outgoing to the internet might as well just be your local machine in the first place - because that's how 'the internet' sees it anyway.
Anyway, I'm all for making DNS more secure...and this seems to be one way to change where your trust lies, but not a definitive solution, to me.