They never specify what he asked them, so it's hard to know.. He might have asked if they use a syringe to access the blood in the vial, which they wouldn't since you can just remove the rubber stopper and have complete (undetectable) access.

Hard to find good pictures, but you can see here: http://i.imgur.com/mhdkpui.jpg some vacutainers (newer, but they work the same) that have been filled, complete with puncture holes. That's just how you fill them.

It's a lot more compelling that the evidence box has been tampered with, in my opinion. You can find a few phlebotomists confirming this in the makingamurderer subreddit, if you look around.