PIDs vs flow IDs

I'm working on a new version of the AR draft and something has come up: how PIDs are not really flow IDs and can change. As far as I know in broadcast TV networks when you use INT with PID, a (re)MUX may re-mark the PID, and then could remark the
INT. This is a standard MUX function. However in a data network I think it is assumed that PIDs are to be used end-to-end (as unidirectional flows), and Muxes should not re-mark. If that is the case it's ok. If it's not the case then we may have to find a way to easily identify flows and map them appropriately.