> "Overall, 340/350 cases of primary cervical cancer confirmed by surgical staging tested HC2 positive (97.2%)." Ie 2.8% (~3%) were considered true HPV negative by this testing.

That study literally explains each of the ten excess you say are "true negative", and only puts one in that bucket. You've made the same error as the author you cited previously. You're conflating HC2 negative ("it wasn't seen in this common test") with HPV negative ("it wasn't present")

They start with 371 smears and access to the patients, in all 371 cases there was also surgical biopsy.

* 340 of the smears say HPV with HC2. So we're agreed those are HPV positive.

* 21 of the biopsies aren't Cervical cancer. If cancer cells from other nearby tissues spread and and we find that in a cervical biopsy that's extremely bad news but it is NOT cervical cancer.

* 5 have non high-risk HPV. HPV-53, HPV-70, HPV-73

* 4 do have high-risk HPV even though the HC2 assay was negative

* Which leaves just one true negative case.

Now the 5 aren't proof of anything, and you can (and doubtless will) argue that it's just a coincidence. Uncleared infections with HPV aren't rare, so we can't rule that out, but equally it is wrong to insist it must be a coincidence. You'd need a mechanism, present only in the high risk variants to explain why these are innocent bystanders or else that's correlation.

The four high risk cases are even more clear cut, that's simply a false negative. Insisting you get to count these as true negative is crazy. HC2 was not adequate to detect the virus here, these patients were HC2-negative but they had high risk HPV anyway, the HC2 assay just didn't see it.