bingoboy - this is not the case. A few years ago they removed the geographical limitation on where AMEs could be appointed and practice. There is now an upper limit of numbers in total.
But all new AMEs need to have either previous or current experience in aviation of some sort to even be appointed. So your class 2 medical could be done by an AME who flies a cub or your class 1 by someone who either works in the industry/military as a doctor or even has their own CPL/IR/ATPL. This is the case for three of the four AMEs in my area.