Is it wrong to over think why Brynden Tully left the party to go to the restroom?
Do you mean that they're implying that he had a hand in it? Because if so, then yes, that is 100% wrong.
I don't know why they brought him, as I've said from the beginning...most likely just to give him more screen time. But my guess is the piss was to get him out of there and ostensibly back to Riverrun.