I didn't say Holmgren is currently playing much of a role, he rode into the sunset, but before he did, the damage was done.
But the idea that Holmgren was Clarke's puppet is silly, doesn't fit anything we know about the man.
I suspect that most decisions were vetted and a general consensus reached, even if Holmgren and then Fletcher filled in the details. Remember, that was a big component of hiring Fletcher, that he'd welcome input from the advisors and make consensus decisions and not be a cowboy.
The problem was probably more a matter of groupthink by a bunch of "hockey men," who reflected the Flyers mantra that rebuilding is for other teams, we "aggressively retool," and always compete. So I doubt there was a lot of heated disagreements until recently, when the blame game started.