You're right, OSU hasn't given me that info. But I did talk to the DGS and she said funding was pretty much assured; they just have to wait for results of the fellowship competition to come in before committing.
As for UCSD, just the way they've handled it is a bit disconcerting. They seem to be pushing us to come visit without giving any details, which worries me. I don't want to commit time and energy to a cross-country trip if funding might not be guaranteed or their offer isn't reasonable. I know it's not completely rational because they'll pay for my stay, but I'd rather not waste my time (and possibly make other more useful visits) if I know I won't be attending.