This is an interesting topic. Epic and I were actually discussing a similar situation via IM chat the other day. I also know of people in this same situation... The skier wants to get better (or at least says they want to get better) but for whatever reasons are not willing to take the steps necessary to make their plans become a reality.
I have actually been placed in a similar sort of situation with my girlfriend (the situation epic and I were discussing). She refuses to take lessons from anyone else other than me. She has several reasons: likes the way I teach her - which is odd for couples, trusts my advice and where I take her to learn, trusts that I won't push her over her head, and prefers to stick with me because I "know her skiing better than anyone else." I've tried to get her to do an ESA - just for the fun/social aspect if nothing else, and her response is, "no - not until I'm better."
I'll never force her to take lessons from anyone else, and I have offered it many times as I know a lot of great instructors and coaches that I could get her lessons with. I have always thought that it would be good for her to take lessons separate from our usual group that we ski with (full of seasoned expert skiers and USSA/FIS/USCSA racers) because her reality of "good skiing" is severely skewed to where she thinks that the ability of a sub 150 point USSA racer is only "average" so she ends up holding her skiing to a higher standard than I think she should... Of course, this same attitude has made her progress in three seasons (maybe 40 days on snow) to being a very strong intermediate to advanced skier. When we ski with some of her friends (who are decent skiers, but not great) she comes home feeling like a hero because she is skiing better than people who have been skiing their whole lives.
So... This might bring another factor to the table. Do the skiers that you normally hang around help to increase your self confidence regarding your ability or do they decrease it? Is it better to have it all one way or the other (skiing with better skiers usually forces you to ski better, but skiing with worse skiers might make you more confident and less self conscious)? IMO, finding a balance for an insecure skier would be important to allowing them to develop their skills unhindered by what is going on in their head.