I'm with Piedmont and I as well as all the rest of our guys would be seriously ticked if a mainline guy or PSA guy took a PDT jumpseat if we were waiting for it. Same as I expect when I'm on one of them that their guys ride before me. That said, I'd be ticked if a non PDT, PSA, or Mainline pilot got the jumpseat on any of our flights because 2nd priority is with the wholly owned-s. Bottom line is that while the computer does not determine who rides, but there are some gate agents who even if you bring it up would refuse to let you down to see the CA... Then maybe you might be lucky enough to wave through the window if there is one or if the CA actually does see you...
Bottom line, they need to fix that problem b/c obviously it is an issue.
Most CAs prob. let someone ride b/c he is the guy who asked w/out knowing their own guy is waiting inside getting the shaft.