"Mere coincidence can be damaging. This occurred in the ill-fated swine flu vaccination campaign mounted in 1976 to protect Americans against what was believed to be an extremely dangerous strain of influenza. Three elderly people, all heart patients, dropped dead on one day (Oct. 11) after getting shots at a Pittsburgh clinic. Experts concluded the vaccine was not responsible, but it took President Gerald Ford and his family getting swine flu shots on national TV to restore confidence in the program -- and even then only for a while." linkI recall the broadcast, and the word was that what the Ford family received on TV was not the vaccine, but sterile normal saline solution.
There had been many claims of problems with the vaccine (which is why the publicity stunt). Would you risk the life of the POTUS, (recall, this was 1976) or his effectiveness over a shot when you can screen persons in contact with him?
In the end, the vaccine is credited with more deaths than the disease.