No, Rasputin would be fine. Probably not RKO-able, but fine from a legal point of view.
It's more the trademark thing I'm a bit worried about.
> sad that copyright owners are this greedy
Not necessarily greedy (though many are), but sometimes just protective. The problem is actually granting permission to do stuff for free might grant unexpected legal rights that they didn't want to grant: not everyone who does stuff for free has pure motives: sometimes it's just pure self-advertising based on the back of others' hard work. Or maybe they wanted to make money, but can't give it away. Or something.
I'm not saying that's what you're doing (in the C64 community we all have much purer motives, I expect

), just that the picture isn't all "bad nasty corporations, heroic little plucky musician". The picture is a little bit more complex and subtle than that. People individually can be just as greedy and venal as the worst corporations, they just cause their damage on a smaller human scale.
And don't forget this is all pre-emptive. In all probability nothing would happen if Tarzan was uploaded, since the problem is generally too small-scale for anyone to care about. The trademark lawyers in my experience tend to be much more active than the copyright ones, though trademark and copyright infringement often go hand-in-hand (but are separate transgressions).
Chris