It seems very funky to me that they want to have close examination of the credentials of firearms trainers but not other types of instructors.
When you go to get your driver's license for the first time do they ask to see your instructor's credentials? Nope. Not at all. In fact you only need to prove that you can operate a vehicle in a safe manner and there is a person there to administer this test.
I'm not a pilot but I wonder if when you apply for a pilot's license if you need to show the credentials of your flight school instructor.
It seems strange to me that one can operate a car without any check on who it was that taught you are required to make sure your instructor in firearms handling has his credentials up to date.