The impression I got from the reporting at that time wasn't that Bungie convinced Naughty Dog to cancel the game. What it seemed like they communicated was the volume of work that goes into supporting a GaaS over the course of many years - the head count, hour count, and spending required. It seemed like they were trying to say "In order to do this successfully, you will have to become a different studio with way more people and a fundamentally different set of skills."
It seemed like Naughty Dog didn't want to give up making single-player games, so they were inclined to back away from Factions.
Ultimately, I'm sure the decision rested with PlayStation. They had to look at it and know if the talent at Naughty Dog didn't want to devote their time to making that game, forcing them to do it would have just resulted in the talent leaving, which wouldn't have made any sense. The alternative was probably "Do we have another studio who could support this game long term if we keep it going?" Again, that's time and money, and reputational risk. They ultimately decided it wasn't worth it.
I'd love to know the details behind who decided Bungie should work on an extraction shooter. Was that a higher up at PlayStation telling Bungie they needed to make a GaaS and they should take a crack at the genre? Was it someone at Bungie who really believed they could make a highly successful one of these? I'm sure the details are pretty interesting.