I know its extremely unlikely (and gfci isn't supposed to be as susceptible to it nowadays) but maybe rf or some other ghost?
If I were to gamble on this one, I'm going with the hooked up line side neutral isnt line side... odds of two gfci being bad are astronomical (aside from previously mentioned returns) older gfci could operate with all kinds of wiring errors, i ran into a kitchen gfci last year that was wired backward on hot (line/load reverse) with crossed up neutrals... still tested and reset and powered downstream receptacles, but wouldnt trip a gfci tester. I made the mistake of assuming it was wired right and just had failed, so when I wired the new one in, it didnt work. Rewired it the right way, still didnt work... the one I grabbed from the truck was bad...wasnt in a box... asked the boss he pulled it from another job... that's why I refuse to put used electrical parts anywhere other than the trashcan...if I dont have one I take a sharpie and put a big X across the face of something like that so I never waste another hour installing a broken part.
It's very easy in a cramped jbox to mistrace a wire. Hypothetically, If there were two circuits in that jbox, using the neutral from one and the hot from the other (both line side), what would happen? I know a GFCI breaker would fail but the receptacle doesnt care about upstream, as long as all the wiring is actually upstream. With no loads connected, either wiring or plugged in, the GFCI should hold. Now, an AFCI breaker will trip if there is a problem even when as small a load as a GFCI LED test light comes on, but OP mentioned nothing of that.
eta: it would be very useful to know how these new self testing GFCI work. I'd assume that they send an x ma signal across from hot to neutral and measure it, and if it's within spec, it goes on its merry way until the next self test. a broken neutral might cause it to fail the test but op said he had continuity between ground and neutral, so that's not it.