Private works entail that no one, or maybe a few people, know of and have a character. If you wish to be broad, if can also mean a character that "legit" mugen sites will not host due to the creator saying that he/she doesn't want his/her work passed around on the internet. However, having a private character being publicly known will, generally, cause tension.
"Illegal" edits aren't, usually, private, moreso they are shunned for being "illegal edits". Therefore, warehousers generally get to pass around privates and illegal edits whereas "legit" sites don't out of "respect" or just because they don't want anything to do with illegal edits. There's also quality control because, from what I've seen, most illegal edits are usually at least one of the following: broken, cheap, very minor edit, or crap.