In this discussion from 2010 on apple.com it says this:
"I can't speak for Apple programmers. If you still have the 3.1.3 ipsw file on your computer it will reuse it and not download it again, but it will still go back to Apple's server to verify the copy that you have, presumably to verify that it has not been hacked."
If you google "verify the restore with apple" you will see it mentioned in a lot of jail breaking related posts. To me this suggests its somehow meant to prevent jail breaking. And perhaps thats what the post in the apple discussion meant by 'hacked'.
To me it also sort of sounds like something intended to prevent people from using stolen apple stuff.
Edit: in addition to what i said in the comments, and to give you an answer with some more finality: Backing up to firmware that you got from a third party may work fine. But theres no reason to believe that it will, other than your own personal perception of the place where you got it from.