No. But they can spread it, possibly to girls who haven't been vaccinated for medical reasons or religious reasons, giving them HPV. It's not about being politically correct, it's about public safety, especially since HPV can give boys cancer, just not cervical cancer for obvious reasons. It doesn't make sense to say you're for protecting against something and then not vaccinating people who can and will spread it. That is, it would be if this was a public safety issue, but since there are other more dangerous things that they aren't focusing on, I doubt it's that.
If the vaccine was safe, reliable, and actually was proven to prevent cervical cancer, that'd be one thing. But it's untested, doesn't prevent cervical cancer entirely, and it isn't punishing someone for having sex if they chose not to get the vaccine. That's like saying that not forcing people to wear condoms is punishing people for having sex by letting them risk STDs. It's each person's choice, not the government's duty to shove its nose in and save people from themselves, or else they should outlaw cigarettes and save smokers and their loved ones from lung cancer.
Whatever your stance on this issue, it's sexual at its very core.