No. I don't know the details of the attack, but a third possibility (as I read it) is that both PDF documents are modified in the process until they arrive at a collision.

PDF has the convenient property that you can inject arbitrary bogus data into the middle of it with a constant head and tail and it will still be valid. The tail of the file contains a trailer that points to the dictionary that describes where all of the resources in the file are located. The entire file need not be covered by the dictionary (and typically won't be for PDFs that have gone through several rounds of annotation/modification). This leaves the opportunity "dead chunks" that can be modified arbitrarily without changing the rendered result.