On the other hand, why wouldn't they hang onto him for a month or so, see if they can't extract information from him (not even talking about torture, there are

On the other hand, why wouldn't they hang onto him for a month or so, see if they can't extract information from him (not even talking about torture, there are much better ways of getting information from people), then ship him back to the USA or send him on his way someplace else. Long-term, he's served his purpose, no reason to spend a lot of money on him, especially if they want to smooth things over with the USA. And that's basically exactly what they're doing now: saying he can stick around until someone else claims him. Whether that's the USA convincing Russia to hand him over or some nation offering him asylum, Russia probably doesn't really care.