Interviews. Many discuss and hint significant GM override, or at least a tier of prospect talent that the GM could select as he deemed fit. Part of it is based on GM criteria where the talent order gets reshuffled based on GM demands. You'd often find that certain players drafted in the earlier rounds had a completely different characteristic profile in the later rounds. Button always found ways to get us talent in the late rounds. You can even easily find anecdotal examples of this happening in other orgs. GMs directly involved in the first few rounds and then sitting back in the late rounds is pretty normal for most organizations.
Sutter often overrode to choose good old rough and tumble Canadian boys.
Feaster and Weisbrod were candid about the Jankowski and Sieloff picks. Weisbrod even spoke about how he himself went to scout Jankowski. There's a Button interview out there that I can no longer find in its entirety that discusses his takes on Kucherov and Gaudreau and how he basically had to sweat it out to the 4th round on Gaudreau because of what Feaster was trying to do.
In Treliving's year 1, it seemed obvious that there was a truculence mandate as I swear Burke ran that draft even past the 3rd round where we drafted Hickey vs someone like Point and we were still drafting tall players into the 7th round.
In Treliving's year 2 and later, it seemed he significantly elevated Button's input a lot more. We saw Button hop up on the podium in the earlier rounds as one of the top dogs more often (if we didn't trade those picks), and we also saw the dude gush about the guys we drafted in the top rounds vs kinda meh in previous drafts. It seemed like Treliving would play the draft odds and relied on his scouts for the odds for reaching the NHL.
It's not to say Button and crew do not submit drafting reports for the first two rounds for all these different GMs. But it seems like the GMs could in theory and often did just run out there and select a guy that excited him the most, scouting reports be damned.
Treliving runs his futures in a manner that he calls currency. He also seems to view games played as a bigger evaluation of appropriate use of currency vs potential. This is why he'd do things like trade Knight for Shore, Sieloff for Chiasson, Kanzig for Lack etc. Minor moves, but it's something from nothing.