The FAA also says that we are responsible to self assess ourselves on rather or not we are medically fit to fly rather we qualify for a medical or not, and if you have failed a FAA medical you do not qualify for LSA. I would not want to be on the wrong end of somebody's mishap flying when they should not be.
It's my understanding that the FAA say's that your aircraft is what you say it is. If you call it a powered glider you can fly it without a medical. You also can fly at any speed and at night. You do have to have a glider endorsement on your ticket.