Only reasons I could see private skins being private is if...
A: As you stated, may have been payed for in some trade, or was a special gift.
B: They personally made it and want to keep their streams and videos unique looking.
C: It's incomplete or may not run well with all clients, as in specially made for them.
But when something is private, it's just private. Whatever reason that is, we aren't meant to touch it so it doesn't matter if we question it.