That is true, but I think what supports the puppet Snoke idea is that Papa Palpy says he’s been every voice inside his head, including Snoke’s.
Sure, but again he’s only saying the voices inside his head. That’s a key distinction I think. Coupled with the other two lines I find it hard to buy that Snoke was a literal puppet, especially when you consider that’s not something we’ve ever really seen in the films - besides arguably TROS where Palpatine is seemingly puppeting his own corpse. But in that case, why would Palpatine need to puppet someone like Snoke? It seems more likely that sort of control is beyond his power, and Snoke was merely a pawn, rather than a puppet.