Story time!

I had blood drawn by a fellow student three years ago, and halfway I noticed he had forgotten to remove the tourniquet. he had his hands full and was nervous enough as it was, so thinking I was being helpful, I told him not to move while I reached to undo it. He thought he was hurting me and pulled the needle back in a panic. No matter what you're doing medically, "panic" is probably not a desirable qualifier.
I wasn't hurt, but it bled because if a vein is shallow, the needle's bevel can have one end inside the vein and one outside the skin at the same time, and a bad technique will let that happen long enough for blood to flow through that space. It's not, actually, a lot of blood, but blood has an enormous mess-making power, and it only takes a mL or two to make a dramatic looking trickle!