No, they won't. Whether or not it was provided by a third party supplier is irrelevant. It does not make disney any less infringing if they are the ones selling it.

It just means you can sue disney, and then disney can turn around and attempt to recover the damages you win from the next guy up the chain.

You absolutely, positively, do not need to sue the people all the way up the chain.

I am an IP lawyer (though this is not legal advice, just an explanation of general concepts :P)