Still false. Maybe if you qualify it further to currently prescribed vaccines (e.g fda certified ones that haven't been taken off the market for whatever reason, or just superceded by newer better vaccines), you'd be closer, but some of those vaccines still wouldn't be recommended to certain people for certain reasons (say after a certain age, or maybe if they're pregnant, or if they have certain conditions, etc, etc, etc)
I don't think it's being particularly pedantic to say "there is no downside to any vaccine" is just wrong, and not really something that should be repeated. It's more of a religious statement than anything else, and it's the exact kind of thinking that comes out of the insane pressure put on people during covid.