I don't think that my dentist could cope with removing my cat's teeth.
It was more along the lines of - it is illegal for a medical doctor to treat any animal other than humans. Yet Vets can legally treat humans. I got first aid from my Vet after my girl cat objected to being weighed.
I paid £400 to get four of Frankie's teeth removed.
If your cat scratched you and your vet gave first aid (eg washed the wound and applied a dressing) then fine. Anyone suitably trained can administer 'first aid'. If however, I needed a surgical procedure carried out, I would consult a medic or dentist rather than a vet.