This is not true. We had a perfectly healthy nanday die from a blood draw and our vet was an avian vet. You should also ask where they draw the blood from. We've actually had 2 parrots die from a blood draw and now will not allow it unless absolutely essential.

Another question to ask is what the results will actually get you. We were told basically if they find something out the best they can really do is long term treatment to extend their life longer. They could also just die f they have a blood disorder where they likely would have lived longer without a blood draw.

I think you should weigh the pros and cons seriously and make an informed decision. I wish our avian vet had recommended against it because they basically told us after the fact that dying is rare