I remember the first time I had my BP taken by a nurse who knew how to position, place, and read my BP properly. I made the comment to her that I am always teaching others how to do so properly and she laughed and said she was very proud of herself because she also saw so many making mistakes and refused to be "that one".
I know some courses in CA also include phlebotomy training with credentialing at the end of course. Perhaps this is why. Aside that you likely won't do any draws in CA, but you should be able to manage at least being around when they are doing them and it sounds like that may be an issue for you.