Apparently the woman only said that she was sick until the airplane had returned to the gate and she exited the airplane.

At that point, probably thirty or fourty minutes had already gone by.

Then five minutes to get in touch with an the right law enforcement agent. Fifteen minutes to get to the plane. Five minutes talking to the woman. Five minutes for the pilot to get the man off the plane. Five minutes of conversation. Five minutes to reboard. Twenty minutes of checklists. Fourty minutes of taxing/waiting.

Since that adds up to more than two hours, it means that the actual process must have been faster.