What they (probably intentionally) leave out to their often cited statistic is that not all of the 95% who leave the AME with a medical certificate get to keep that certificate, at least not without additional paperwork.
What I’d like to know is how many of those 95% are later found to be “invalid” at OKC. And then how many of those are then reinstated. If the latter is anything other than 0 (and I know it’s a non-zero number), it would tell me that the AME who actually sees the pilot knows more about that pilot’s health than some faceless doctors at OKC.
The FAA still has a lot of work to do to modernize and streamline (for the pilots) the medical certification process.