TL;DR: We have no idea if they were real, and if they were what caused them, and it's ok to be unsure and inconclusive sometimes.
That a succession of women served as Oracles in the Temple of Apollo (for hundreds of years) is well supported.
Accepting that we won’t know everything (but also accept that there are things we don’t know yet and that will be known in the future, and that it’s ok to change your mind in the face of new evidence).
Actually, it’s not really an alternative to empiricism, but I don’t thing that empiricism has this particular weakness.