Even though HPV is considered a cause of cervical cancer, only one out of 1,000 women with HPV develops invasive cervical cancer (ACOG, 2000). Most HPV infection never leads to the development of cervical cancer even in the absence of medical intervention and treating precancerous cervical lesions detected by Pap tests has greatly reduced the rate of invasive cervical cancer (Ho, et al., 1998; NCI, 1999a).
If the result of vaccination is fewer pap smears then it could have the opposite effect than intended.
Those number can be completely correct and yet have HPV be the primary reason for cervical cancer.
If more than 50% of women have it and one out of every thousand who have it get that cancer, then it could very well be the sole reason.
That's an awful lot of women in that number.