The test that the Sport Pilot and the CFI have to take are FAA tests. Written and practical, it's FAA mandated. With a parkflier you can buy and fly without ever having heard of the AMA. Sorry STL, (not really) but your analogy isn't relevant. The FAA "gate" he's talking about is real. You can't get a SP certificate without ever having heard of the FAA.
How did we even get to this. You think I don't know this? But the point is that the AMA did in fact mold the e-ticket off the SUCCESS of the EAA/FAA's Sport Ticket which is very successful. Sorry but you guys just don't understand niche markets and how and when to strike.