"oh nice, a youtube-link from one of my sources, let me get my camera set up to archive it ..."
I kind of expect a serious investigator to archive these materials just for the sake of it. I don't expect them to make it harder on themselves for no good reason.
Filming the screen, means that in order to fake it, you have to setup something that routes youtube.com to your own fake version of youtube, before filming. To me, that sounds much harder than say "this file was downloaded from here on that date"