Information from the CDC [1], indicates Adverse Reactions are similar to administration of a placebo, which is not zero. Any vaccine administration has potential for negative adverse reactions, it's reasonable not to get a vaccine if you judge the upside is not worth the downside, even if the downside is small.
The CDC says:
> Like all medical interventions, vaccines can have some side effects.
> A temperature of 100°F during the 15 days after vaccination was reported in 10% to 13% of HPV vaccine recipients. A similar proportion of placebo recipients reported an elevated temperature.
If you take some research subjects, do nothing to them, and then ask how they did 15 days after, I would be surprised if 10-13% reported a 100F fever during that time. But, that's a reasonable result from a saline or hpv injection.