So far in this life I have had blood taken only twice (excluding the numerous obligatory blood tests that I was subjected to as a prem baby). I thus realise that I may not be the most able to judge what is and is not correct policy on this matter.
When I first had blood taken, you wanted four vials. I could not give you four vials, because I passed out halfway through the second. I am half an inch under five foot and weigh 90 lbs, making me both tiny and very slightly underweight, with low blood pressure. It did not come as much as a surprise to either myself or my mother who was there with me that I passed out.
The nurse was not pleasant, but nor was she nasty; the service was adequate, until I (shakily) informed her that no, I would rather not have any more blood taken right now, because my body was rather obviously not equipped to handle it. She became rather stern, informing me that 'well, we won't be able to do all the proper tests!' and acting in a thoroughly disapproving fashion. Bearing in mind that I had just passed out because of blood loss, this did not make me feel charitable towards her- I felt that she was implying that I was at fault for being too delicate to have that much blood taken. She was not absolutely dreadful, but I found her response abrasive and rude.
The second time, it was rather better, mainly because of the very sympathetic phlebotomist. I was about five seconds from having a needle plunged into my arm, when I explained to her that I had been known to faint in blood tests, so could we do anything to improve the situation? Her response was surprise: no-one had told her! I was equally surprised that no-one had thought to make a note on my medical file- they certainly seem to have everything else on me in there.
(The situation was quickly resolved by the needle being removed when I began to feel nauseous (a warning sign for fainting), having me lie down on the bed and have the needle inserted into the other arm. All in all, a much better experience).
TL;DR: Delicate girl faints during blood test, nurse gets shirty when girl decides not to have any more blood taken that day. Next phlebotomist completely unaware of this, due to lack of any note made.
It's not nearly as bad as some of the things posted here, but I felt quite irritated about it at the time, and I'm glad to get it off my chest.