Two years ago, flying UX out of YYZ, I was paged in the MLL at T-35: "If you're on United flight ???, your airplane is boarding NOW for an immediate departure!"

I limped at top speed for about 5 minutes to the gate, and the plane pushed about 30 seconds after I boarded. I must have looked completely deer-in-the-headlights when I asked the FA what had happened, because she started laughing (in a nice way). Turns out, the flight arrived early, and there's a limit to how long they can sit on the ground without forcing the the crew to clear customs. So it was a choice between (1) leaving at T-29, or (2) taking a delay while the whole crew got off and cleared customs.

Fun times...