From what I’ve heard, this misconception comes from the CDC’s Vaccine Adverse Event Reporting System (VAERS). Pretty much any issues that come up after a vaccination are reported to the system. Using that data, the CDC can detect side effects with extremely low rates of occurrence. Since vaccines are administered to the entire population, it is critical to detect these issues because even problems that are unlikely to arise from an individual dose will result in widespread harm.

Unfortunately, people who don’t have an intuitive grasp of statistics have full access to VAERS. They will cry foul when they see thousands of deaths without realizing that those deaths have no relationship to the vaccine nor any particular similarity to each other. They are simply records that are there to ferret out any issues that were not detected in trials. That then goes viral on the Internet without even less context and reaches people like your friend.