If one person in a million falls seriously ill after the vaccine, that does not mean the vaccine has a one-in-a-million risk. To find the actual risk, you must subtract from that one-in-a-million the risk of falling seriously ill without the vaccine, a risk that is surely at least one in a million. For true statistical accuracy you have to control for the likelihood that a person with a certain risk of illness will get the vaccine.
You're making my head hurt.