Only stick in AC

I didn't question her further because I didn't want to seem rude, but I am genuinely curious if/why certain healthcare workers are only allowed to draw blood from the AC.

Perhaps a facility policy. Perhaps the tech misinterpreted what she was told. She may have been told something along the lines of "try the AC first, since there is a big vein," which she took to mean "only stick someone in the AC."

If you have questions regarding the medical care you receive it is normally best to ask to speak to a supervisor in the facility in which the event happened.

Although I'm a nurse, I'm not experienced with lab draws since our nursing school didn't teach them, and my current position doesn't require them. But something doesn't sound right about this. If this person didn't go to school for phlebotomy or nursing, then what training DID they receive? Maybe their position has on-the-job training, but it doesn't sound like it is adequate if they are only able to draw labs from only vein. If they're not willing to listen to you, and are continuously unsuccessful, you could always ask for another tech.