Far be it from me to question the legal advice handed out by a receptionist at an optometrist's office, but I don't think that's even close to being right. In fact, during my last annual physical my doctor asked me whether I'd had the shingles vaccine (I had) because he couldn't remember.
When the scheduling people at a health care facility talk to you leading up to an appointment, all they are interested in is whether you presently have covid. Have you tested positive or been in contact with someone who has tested positive. Those questions are just for the purpose of letting you in the door. Whether you've been vaccinated or not is irrelevant for that purpose.
Now, when someone goes in for the actual physical, I wouldn't be surprised at all to hear that the doctor asks about whether the person has been vaccinated for covid, assuming its not already in the records.