I kinda figgered that might be the case, but wasn't sure.They turn away anyone who can't provide a good vein in the usual place. They don't want liability issues if they ruin the only good vein a person has left.
with what you've been through, I'd probably be squeamish too! They used to dig and put me through torture til I was in the Navy, and I asked the guy if he was good.......he said.......I never miss, because if I don't know that I can get it, I don't do it there. He looked at my arm veins (antecubital......did that give you a rush?) hehehe and said........I aint touchin you! lol He actually did get it, but used a butterfly needle and took it from my wrist. After that I started making em to IV's and draws from my hand or wrist.A lot of it seems to come down to how competent the individual is in dealing with someone that doesn't have steady (non-wiggly) big veins.