Is it possible that they can't give her the vaccine because she misrepresented herself on her appointment application and therefore they can't verify that she is who she claims to be?

If Jane Doe says, "I'm a white person named Jane Doe who wants this vaccine," and then a very clearly not-white Jane Doe shows up for the vaccine, the healthcare workers can't verify that this is actually the correct Jane Doe, because her demographic information doesn't match her application.

This sounds more like they're trying to avoid a potential fraud situation by giving the scheduled vaccine to someone who is not accurately represented by their application paperwork.