Regarding info on CDC website

I understand your confusion, HPV is certainly not a very black and white and or clear cut disease. The best answer I've found to that question is found here http://ehealthforum.com/health/info-on-hpv-t173358.html and the man who wrote it has probably the most credibility when it comes to the subject:
Q11. What about all the people you hear about on the web forums and chat rooms who insist on new research challenging the clearance studies, they say that HPV has no "cure", is this true?
A. There is no "new" research indicating that HPV persists for life or that it doesn't. The suspicion that it sometimes (often? usually? always?) persists has been present for 20 years and to my knowledge there is no knew knowledge that provides clear answers.

And about "cure", one problem is terminology. What does it mean for an HPV infection to persist? If a snippet of DNA has been integrated into the host cells, but not enough DNA to result in viral replication, does that count as persistence or cure? If the virus's full DNA genome persists but the immune system successfully prevents it from replicating and causing warts or pre-cancerous changes, is that persistence or cure? What if there are whole virus particles, not just DNA, but something (immune system, DNA regulatory mechanisms) keeps it from ever causing a problem?

So the biology is uncertain. But some of the epidemiologic facts are clear. Once HPV clears up, it is rare for that particlar infection to either cause problems in the future (warts, pap smear changes) or to be transmitted to a sex partner. And once a person has cleared a particular strain of HPV, the immune system makes it rare to catch that HPV type again. But "rare" doesn't mean these things never happen; they do.

From a practical standpoint, my view is that most people can consider themselves cured when all signs of their HPV infection are gone, there is no recurrence within a few months (and certainly within a couple of years), and the available tests do not detect the virus. Undoubtedly some people with those outcomes still carry viral DNA. I consider them cured, and I encourage affected persons to act accordingly. It is precisely because of the emotional impact that I lean toward using the word "cure"