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The FDA reporting she's talking about is an uncontrolled system that does not discern real from coincidental effects and is considered close to worthless by people who are in the field. Here's an excerpt from a contolled study of thousands of patients published in the New Engl J of Medicine last year:

There were relatively few side effects of vaccination. The proportion of subjects who reported one or more injection-site adverse events was higher in the vaccine group than in the placebo group (84.4% vs. 77.9%), with the most common event being injection-site pain (risk difference, 6.5 percentage points; 95% CI, 1.4 to 11.7) (Table 4). One subject in the placebo group discontinued participation owing to a serious injection-related adverse event (hypersensitivity). The proportions of women reporting serious adverse events were similar in the two treatment groups. (All systemic and serious adverse events, categorized by organ system and treatment group, are provided in Tables 5 and 6 of the Supplementary Appendix.) Within these categories, there were nominally significant differences in the percentages of subjects in the vaccine group and the placebo group who reported seasonal allergies (10 in the vaccine group and 2 in the placebo group [risk difference, 1.8; 95% CI, 0.3 to 3.7]) and neck pain (2 in the vaccine group and 10 in the placebo group [risk difference, –1.8; 95% CI, –3.7 to –0.3]). No multiplicity adjustments were made for these comparisons. Adverse-event profiles were generally similar for women with and without antibodies to one or more of the vaccine-related HPV types at enrollment.