As soon as the next group of commercials came on, that was the first thing I asked my wife about.(she's an NP) Paraphrasing here, but she said it was totally possible, especially if the person doing the biting had a good set of teeth. I followed up with your exact question regarding muscle/tissue, ect. She said that artery is very exposed just under the skin, and wouldn't require a 'deep' bite. If the person knew where to bite, it could be done, and the scene wasn't unrealistic.
KoRn, I remembered that post but not the author. Sorry...otherwise I would have courtesy pinged you on #25.