They can offload you if you do not board by T-15, but that doesnt mean they are required to. They check to see if you're flight just arrived and judge if they think you will make it. Sometimes depending on number of pax left, your status, etc they'll wait or even delay the flight. Its a judgement call. By "they" I mean the gate agent and their management. There are things that can be done to move the push back time but still keep their take off slot. Also, the flight could already be delayed for other reasons (weather, mechanical), meaning even though you arrived after the orig T-15, the flight was actually delayed.