They're completely wrong, and are using it as a bullshit (excuse my language) platform to push their "moral" righteousness.

This simply proven:

  Based on data from 2006 to 2010, about 33,200 HPV-associated cancers occur in the United States each year: about 20,600 among females, and about 12,600 among males. Cervical cancer is the most common HPV-associated cancer among women, and oropharyngeal cancers (cancers of the back of the throat, including the base of the tongue and tonsils) are the most common among men.

That's from: http://www.cdc.gov/cancer/hpv/statistics/

Now let's quickly look at how many cancer cases we're looking at each year:

  In 2016, an estimated 1,685,210 new cases of cancer will be diagnosed in the United States and 595,690 people will die from the disease.

From: http://www.cancer.gov/about-cancer/understanding/statistics

So I don't know where they got their numbers from.

You might also be interested in: http://www.aicr.org/research/research_science_policy_report.... -- which has a pretty great rundown of preventable cancer incidences. Quite interesting, really.