I'm not a conspiracy theorist in any way and I have had all my vaccines to date, but I had the flu shot once due to the recommendation and I had never been so sick in my life.
I know that the virus is weakened/dead and the odds of catching something else at the same time is high, but the area I had received it was so inflamed and the symptoms I had gotten all seemed in line with the flu, that I wondered if I had not weakened my immune system a bit by giving it something additional to deal with.
Still pro-vaccines, but I can understand how people relate bad experiences to these kinds of things