No doubt this will be the case for some. So, you've found a logical flaw in people's stated reasons for not wanting a vaccine. How does that help anything? In these kinds of debates, the actual goals or beliefs of both sides often differ from what they say.
For example, the government being able to tell you what to do, vs. it not.
People end up locking in to trivialities like approval or some study, but they just obscure the real debate. Doing more to get the tradeoffs we are making into the open, and talk plainly about what people are being asked to do, why, and what their rights and options are, is much more valuable IMO than trying to find clever flaws in the reasoning of either side. Flaws are there, and obvious, but generally not central to anyone's core thesis, and almost certainly not going to sway anybody. They just let people score cheap shots against their opponents and pump up their own supporters.