That doesn't explain why the GFCI outlet isn't working. it should still pass current even if the upstream stuff is messed up.
Presumably, it's not working because the upstream stuff that is messed up isn't passing current due to a bad connection. It's common for these backstabbed outlets to be daisy-chained through the backstab connections (see the photo above for an example).
The sort of electrician that uses backstab connections is also the sort of electrician that won't bother to pigtail.