In the case of Polio, the original vaccine has this said about it “The vaccine actually induced 260 cases of poliomyelitis, including 10 deaths.”
Was the benefit worth the cost? If you could save 1,000 lives, would you sacrifice 1 through statistics? Like anything else, it’s a game of benefits vs risk.
Someone, somewhere is going to die from getting a shot. The question at the end of the day is did I do any harm? Are there people who are going to be alive in a year or two, who would have been statistically dead if I did nothing?
To answer your HIV question of 5% fatality rate; first off this would NEVER be approved by the FDA. But if it were, you would ask yourself - what are the odds of me catching this bug? If I catch it, will I die? Will I take out someone innocent?
If this were “Night of the Living Dead” scenario, and an anti-zombie vaccine had a 5% fatality rating, would you take it? I would. It all depends on the situation.
Besides, I like my meat med. well; not rare.
The distinction you are missing in your example is whether you forced them to take the vaccination which killed him. It is the difference between an accidental death of someone who chose to take the shot and the pre-calculated murder of someone who was forced against their will to do the same.