Perhaps they mean in the long term? I've met people who wanted to wait a year or two before trusting the vaccine because while we know it to be safe in the short term, it's impossible to know if there may be more subtle effects seen on the years to decades scale.

I got mine and was fine, my bf isn't getting it because he already has natural antibodies from an infection early 2020, and also he's at high-risk for one of the more severe side effects due to a hereditary condition.

He was concerned about getting the vaccine anyway before it's fully approved because of the reasons I listed above. I personally I doubt it'll be an issue but it was a real concern from his point of view so I respected it.