I think you are absolutely right to be concerned. Not because I'm anti-vaccination, but because I think that this is a very weird way to market a vaccination, and I do not think it's necessary, not even as necessary as rubella or measles. It doesn't prevent cervical cancer, it only prevents about 4 different kinds of targeted viruses from replicating (the rest are left alone) that are identified causes of cervical cancer and honestly, this is not a deadly cancer to get.
My daughter will not be getting this shot unless she decides, at a later date, that she wants it. Luckily we have about 6 more years before the "pressure" will be on, and by then we will have a better idea of how the vaccinations hold up over a longer time in very young children.
She will have regular visits to the gyno, since I am a western medical preventive treatment nerd.
I'm no prude, I think kids need to know all the health hazards and happiness that comes with a robust and active sex life, but I do not think that vaccinations fix everything, nor do I think they are always compellingly necessary. For example, there was one person lower down who said HPV is not the regular wart on a hand. Actually, that's all a papilloma is. A warty growth. Lots of viruses cause it. The cauliflower looking ones that can invade the genital region could grow anywhere under the right conditions, they just like mucus membranes and darkness. Lots of different ones like to grow in there, and they only show up sometimes with a swab of white vinegar and a blacklight. That's why you need a pap smear, to check for precancerous cells, which could actually be caused by any number of things (not limited to the 4 warts they can vaccinate against.) Sorry, but this is just not worth it. If they increased the vaccination strength by about 50 with no undo health problems, cool. I'd consider it. Your daughters should all still go to the doctor for paps regularly though.
And I don't think anyone has done anything "wrong" by insisting their girls are vaccinated. I think that if you have dealt with this sort of thing in your own life that you are more interested in keeping your girls safe from the stuff you faced. I just think it's a personal choice, and my current choice would be "no."
If my kid decided to have sex, maybe we will consider it at that time. But I am not going to be overalarmist and have her vaccinated for one of the most survivable cancers known to mankind that is triggered by only a few of the many types of wart viruses that have evolved to plague us. I could see a "vaccine expo" as a great way to get kids vaccinated if they were, for instance, vaccinating against against breast cancer or herpes or HIV. So, if they come up with those ones and mass market them to my kid when she grows up to the tween years, then we're sold.
I seriously do not equate gardisil with the smallpox vaccine. I also laughed when I read that someone else said you get HPV from multiple sex partners, oh lordy. When will we learn that all it takes is once? That said, I'm still not interested in my kid getting vaccinated for it.