I think screenshots are a good start to prove that conversations, disputes, and so on actually happened, especially when there's not a whole lot of choices. But it's not completely solid, because editing words on a webpage is pretty easy.
As an example, I am presenting screenshot proof of my long-held conspiracy theory: That /u/Vendor_BBMC is the real Dread Pirate Roberts, and he paid off Ross Ulbricht to go to prison for him.
Look: https://www.anony.ws/i/2015/12/21/PROOF-Copy.jpg
Well... there you have it, folks.
Easily the best part.
=)