Here's some helpful things to know:
Don't expect your friend's anxiety to respond to logic or reason. Anxiety and fear are often triggered by the Amygdala, the primitive part of the brain that initiates the flight or flight response. When this part of the brain dumps a flood of adrenalin into the system, you feel a response that's good for survival, but not always pleasant. Picture walking around a corner and seeing a Bengal tiger. Adrenalin rush! Or it can be fun, like Bungee jumping. Context has a lot to do with it.
Things go wrong when being confined in a sleeping bag (or spiders, snakes, heights, etc.) stirs up this survival mechanism. It may not be logical, but however the mental association occurs, it feels very real to the person who's experiencing this. Now you can go into a psychological process called "desensitization", where you're gradually exposed to the stimulus which provokes the anxiety until the response abates (is extinguished) but that's rather involved, and likely unnecessary. Of course, your friend could practice using a sleeping bag at home, in comfortable, familiar circumstances. That would be similar.
Practically speaking, it's probably better to go around this problem than through it. Quilts are great, and becoming more popular all the time! Katabatic and other companies make quilts which are much less confining, but are warm down to zero centigrade. That could be an easy solution for your friend, if that's actually the main source of anxiety. Keep in mind how, especially for newbies, sleeping outdoors itself can stir up a bit of trepidation. Also hunger, dehydration, fatigue, gaining altitude too quickly, caffeine, etc. can contribute to feelings of anxiety
There was a recent post on this board about sleeping bags vs quilts. A large percentage of backpackers expressed unpleasant feelings of confinement, anxiety, claustrophobia, etc. with mummy-style sleeping bags. Personally, I don't like the restricted feeling of using a mummy bag. I use my mummy bag as a quilt most of the time, even when winter camping. Now the funny thing I've noticed, when it gets colder as the night goes on, it feels much more comfortable to zip up and snuggle inside the bag. So go figure.
I've worked as an addiction counselor, and for anyone having problems with anxiety, I would not recommend jumping right onto the medication merry-go-round. The side effects can be noxious and unpredictable. There's a good self-help book called "The Anxiety and Phobia Workbook" by Edmund Bourne (New Harbinger Press) that describes very sound principles for developing an integrated, lifestyle approach to dealing with anxiety. For serious, recurring problems, "Cognitive-Behavioral Therapy" is a respected, sensible therapeutic method.
I certainly hope your friend doesn't think they have to give up the glories of backpacking in the Sierra just because of the commonplace, unpleasant experience that many people have with mummy bags.