This is exactly why it's so important to only take your birds to either a Certified Avian Vet, or an Avian Specialist Vet that only treats birds. Most General Vets are at least honest and responsible enough to say "Nope, I don't see anything but dogs and cats", or at the very least "Well, I can see your bird, but if he needs any testing done at all beyond a Fecal Culture, I'm not doing it!". However, a lot of "Exotic's" Vets either know they aren't able to perform certain tests and procedures on birds and some reptiles, or they think that they are able, either way the end-result always seems to be that the bird doesn't get done what it needs.
If a Vet tells you that they cannot do a simple, routine blood-draw from your bird's neck, or they make-up ridiculous excuses as to why they can't do a blood-draw, or try to tell you that "it's not safe to take blood from a bird", like they did in this case, then you simply are not seeing a Vet who is qualified to treat birds, and you need to leave and find the closest Avian Specialist to you. And if you have to drive a few hours one-way to get to the closest CAV or Avian Specialist to you, then that's what you have to do, and it's well worth the drive.
I've seen my CAV take blood from my birds many times (they all have blood work done once a year during their wellness-exams), and it's not at all a big deal. In fact, the actual physical exam of the bird where they look all over their body, under their wings, around their vent, checking their feathers and their skin, looking in their ears, eyes, mouth, and nostrils, etc. is much more stressful and much more of a big deal than the blood draw from the neck is. He literally picks the bird up, gets the bird positioned in his left hand with the bird's head clasped between his finger and thumb, he uses a little water to wet the feathers covering the vein and split them apart so he can visualize the vein, he wipes the area with an alcohol swab, he sticks the needle in, takes the blood, and is done in less than 15 seconds or so. That's it. And as already mentioned, the puncture closes right up on it's own, just like when we get blood taken. It's no more invasive than when we get blood taken from our arms. And they lose only the blood that is collected for testing, that's it. So any Vet who says otherwise simply doesn't know what they're talking about, or they are making excuses because they don't feel comfortable doing it, and if this occurs then you shouldn't allow them do it anyway.
And as already mentioned several times, even thought doing a blood-draw from the neck vein is not that big a deal for a bird, they do still have to be restrained by the Vet, and they do still have to have a needle prick, etc. So if you're ONLY having to get blood from your bird for a DNA test, that's it, and you're not having any other blood-work done at the time, then you do not want them to do a blood draw from the neck. It would be totally unnecessary to put your bird through the stress of being restrained and having a needle prick, etc. simply for a DNA test; also, there's no need to do a blood draw from the neck for only a DNA test, as a DNA test only uses a single drop of blood, that's it. So even if you have a very good, experienced Avian Specialist Vet who knows how to do a neck blood-draw from a bird, there's still no need to do so for ONLY a DNA test, as they would be taking out much more blood than needed for the DNA test, and probably just disposing of the rest. ****A simple toenail clip is absolutely the best way to collect the drop or so of blood needed for a lone DNA test. Clip, collect a drop or two on the card or the swab, then clot with Qwik-Stop, and the whole thing is done in 1-2 minutes. That's it. Or they can do a feather-test. Either way, there is no need to do a blood-draw from the neck...
***However, if you want to get your bird DNA-tested and your bird has never had routine, baseline blood tests done, then be smart about it and take advantage of this opportunity. You should have your bird go through a wellness-exam at least once a year, and ideally that wellness-exam will always include routine, baseline blood-tests, such as CBC, DIFF, CHEM7, Coags, and then also liver and kidney functions. These are just the routine, basic blood tests that will rule-out or confirm infection, anemia, etc., as well as assess your bird's liver and kidney health. This is the best way to stay ahead of your bird's health, as we all know we cannot rely upon them to show us that they are ill. So, if you decide that you want to get a DNA test done on your bird, then take advantage of the situation and have them run a complete, baseline blood work-up. Or, if you're getting your bird's yearly wellness-exam blood-work done, and you've thought about getting them DNA-tested but haven't ever gotten it done, then take advantage of the fact that they are already going to be doing a neck blood-draw, and just have them add the DNA test to the blood-work.
I dont know about that. Yikes. 
