Only youre refute is just as baseless as the original post, tbh.
We don't know how long Chester has been adrift. He could've been pulled to that timeline long enough to see what was going on, not a far fetch since most bloodborne persona are of a scholarly and inquisitive nature. He also has the other peice of the pendant, meaning he MIGHT know other things about it's nature and origin. Maybe he is from bloodborne and obessively studied an 'arcance' pendant till it pulled him to another world. Also not ALL hunters used guns or conventional trick weapons, Simon used the Bow-blade and Chester does have a suped up crossbow unlike any we come across. He could've lost his gun or lost a means to create bullets. That's the thing about speculation-lore, there's always a possibility in the unlikely.
Think of it like this, you already play as a character existing in multiple universes, You summon and invade other CHOSEN UNDEAD, living the same exact destiny as you, really you're just invading and summoning alternate versions of yourself, by the games own logic to explain the occurance of multiplayer. This implies an accessible existence of the multiverse in the Dark Souls reality, that Manus is revealed to beable to manipulate, (As a side theory, only humans can interact with other 'worlds' making the "Primeval Man's" power much more explainable.) With a canonical lore, It's still completely possible that Marvelous Chester is from the Bloodborne timeless via countless other explainasions than your own; no proof either way, so if it's POSSIBLE, why not?