Is there any sort of statistical analyses which could give some idea of whether those bits were generated randomly, by a human, or perhaps came from some other key?
They are just 256 bits. And if they come from a cypher they certainly can't be distinguished from the pure random bits or from the bits from any other key.
But if they come from some other key unmodified it would be possible to scan for the match, and it's a fast operation, as soon as we have the keys in which we'd like to search.
I was wondering about the possibility of distinguishing between a human opening a keyfile (I believe they are encoded in base64?) and manually overwriting pieces of it with random rubbish, or something else; humans make very poor RNGs, as anyone who has tried "randomly" mashing a keyboard will notice.
Please resist complaining about downvotes, as the site guidelines ask. Most unfairly downvoted comments get corrective upvotes after a while—that's what happened in the GP's case. Comments like this one, though, just add noise.
But if they come from some other key unmodified it would be possible to scan for the match, and it's a fast operation, as soon as we have the keys in which we'd like to search.