OP, I understand where you are coming from. It does sound like the GA was somewhat unclear.
But just as I get to the airport on time even when my flight says it will be delayed, I would never leave the gate that close in, unless the bathroom is within site of the gate, you can go quickly and they haven't started boarding yet.* I don't think you would have been due any compensation outside of being put on the next available Delta flight.
Mike
*Those of us with kids know that, no matter how many times you pee the kids before boarding, there is something about a boarding announcement or a "fasten seat belt" announcement that makes a kid have to go to the bathroom. I can't speak for anyone else, but mine are forced to wait until we are on the plane.