Correlation is not causation.
If there is a 1% chance of a particular medical event occurring each week, and 1000 patients receive a vaccine this week, 10 of them will go on to experience that medical event during this same week. This does not mean that the event was caused by the vaccine. In this example, ten patients experienced the event last week, before they received the vaccine. This does not mean that the event was precipitated through anticipation of receiving the vaccine.
Which is why the connection needs to be investigated, not dismissed. You eliminate Gardasil as the cause simply because you wish it to be so.