Why does our Port Arthur ceiling stain sit two rooms away from where the roofer says the leak is?

Because water commutes. On a pitched roof it runs along rafters and decking seams downhill from the entry; under a flat membrane it travels laterally until it finds a fastener or a seam of its own. The stain marks where the water arrived, not where it entered, and the local craft formulation is exact: the entry point sits uphill of the stain. This is why tracing is the first purchase and patching the stain's location is money spent on geography the water never visited. The roofer's scope should name the entry component, and after the next driven rain, that is the claim you can check.