Well, I respectfully disagree. Not saying the pharma companies aren't sometimes (often!) driven by dodgy motives, but I think HPV and H&N cancers is a genuine thing, albeit smoking and alcohol are more common causes. The good news is that HPV-associated H&N cancers are associated with a better prognosis/easier treatment than others.

This paper is from 2011 and the incidence is growing if anything (though will hopefully reverse as the immunisation effect kicks in):

Over the last decade it has become clear that human papillomavirus (HPV) not only causes genital and anal cancers, but also causes a subset of head and neck squamous cell carcinoma (HNSCC). In addition to the estimated ~492,800 cervical cancers caused worldwide by HPV each year, HPV also causes an estimated ~30,000 oropharyngeal cancers, HPV is detected in ~25% of all HNSCC (Kreimer et al., 2005), and the majority of these HPV-associated HNSCC are oropharyngeal (tonsillar and base of tongue) squamous cell cancers. In fact, HPV is now the major cause of oropharyngeal cancer in developed countries, detected in 45–90% of cases (Fig. 1) (D’Souza et al., 2007a; Kreimer et al., 2005; Nasman et al., 2009). HPV has also been detected in a smaller subset of laryngeal (24%) and oral cavity (23%) cancers (Kreimer et al., 2005). There is strong and consistent molecular evidence demonstrating that HPV is an etiological cause of these oropharyngeal cancers. HPV is detected in the tumor of these oropharyngeal cancers, where it is localized to the cell nuclei, transcriptionally active, clonal, and not found in the surrounding benign tissue (Gillison et al., 2000). Epidemiologic evidence for the role of HPV in oropharyngeal cancer is equally strong. Case–control studies consistently show that oropharyngeal cancer cases have a higher average number of lifetime sexual partners (a surrogate for oral HPV exposure) and are more likely to have current oral HPV infection than matched controls (Gillison et al., 2008a; Heck et al., 2010; Schwartz et al., 1998).

Nearly 100% of people with cervical cancer had worn a skirt in the previous year, but that doesn't mean that skirts cause cervical cancer..

It is not at all surprising that 70% of (typically older) adults with oral cancer have HPV-16, because that's more or less the basic prevalence in such people.

I would be astonished if many more of them did not smoke / chew tobacco, either currently or with a long history of it... because that's the biggest cause of oral cancer. Alcohol use is second.

Anything saying otherwise is marketing. Or, in the case of Michael Douglas, mistaken and the claim he made repeatedly when he got it was withdrawn.