Ok, so I watched some of that video and there is a comically simple explanation[1] that throws a wrench into Binney's "proof". All he knows is that the files were at one point saved using a FAT filesystem. He doesn't know specifically when that happened and if it was before, during, or after the documents were stolen.

[1] - https://www.youtube.com/watch?time_continue=593&v=mwUoE8UecC...