From my personal experience and what I've heard online, that seems like wishful thinking. I know two people who had bad heart reactions to the vaccine whose doctors insisted it couldn't be from the vaccine and wouldn't speak of it being connected. And it seems like I've heard similar stories online dozens of times. My guess is the VAERS data dramatically undercounts incidents.

The Pfizer whistleblower paper claimed that even in the early days of the vaccine, internal Pfizer incidents weren't even reported. And given how hostile the entire internet is to discussions of vaccine safety, the idea that people are extremely reluctant to report vaccine injuries seems believable.