the ucsd website most definitely states that they do not give athletic scholarships and that such scholarships are contrary to the school's history and tradition. However, perhaps they find other means to provide funds to student athletes who are otherwise qualified for need or merit based funds as the other posts suggest.
Our own personal experience shed no light on this as the recruiting coordinator we dealt with was an absolutely horrible communicator and obtaining a straight answer on just about anything was impossible. However, I do not believe he is with the school any longer. Beyond this, we received very mixed messages about the level of satisfaction with this program from two former players so
It all struck me as a matter of personal taste and worth exploring. Never met with or spoke to other coaches there so can't pass judgment. They seem, in general, to have a pretty successful program. They also have summer camps that might be worth checking out to get a first hand feel for yourself.
In any event, UCSD is a very well respected school, academically and it is quite a challenge to be accepted there, especially for out of state students, from what I am told. It is in a beautiful location.