You are correct on face value. But the context is different.

OP is posting a lot of material with titles that intend to create a narrative of vaccine danger that does not actually exist in the publications.

> The vaccine isn't good for everybody. That's all this is saying.

This is written weakly. Your writing suggests, to be literal "The vaccine is bad for some people." That is deceptively alarmist.

A better description might be "The vaccine is good for everybody, except for very few with specific health issues." I don't mean to be pedantic, but my point is that the data on vaccine outcomes is much more overwhelming than "It's not good for everybody".