What does the tester do on other outlets? What kind of
tester is it? The kind with the 3 lights? I don't see how
that kind of simple tester could show a missing neutral
and have the outlet work, which it obviously does.
The GFCI and outlet would work with the ground and neutral
reversed upstream of the GFCI. However I don't see
how the basic 3 light tester would figure that out.

If the tester does the same thing on outlets on other
circuits, then it's a bad tester. If not, then we have a
mystery.....