google "GBS swab instructions" - you can see a pdf which categorically tells you do do it that way (the entry hole then the exit hole).

but it's probably one of a million things that at the end of the day, different hospitals do different ways

I didn't bother with the test with DS1, but someone here shared a story of a very late loss from GBS after DS1 was born, so I did for DS2.

strange swabbing requirements notwithstanding.