@varx
That's my take on it, yeah. Kind of a sensitization reaction, that is reinforced every time a blood draw is needed. If a person is prone to anxiety, it seems to ratchet up even faster.
I've seen similar cycles with young kids, albeit not with fainting per se; that does sound like an extreme case, but perhaps a difference of degree, not kind. About 1/3 are just "yeah, this is normal, right?" when they're getting poked and prodded constantly, because it's all they've known. They still don't like it, but they recover quickly. The other 2/3 are fighting for what they assume is their life, because they're that terrified of getting poked. It's a very hard cycle to break.
Also: medical folk can often forget how invasive venipuncture is. There's a good reason why we don't have natural ports to the circulatory system, and the body really aims to keep it that way. I really try to approach anxious people with a lot of care and sympathy because of that.