Does it specify what her degree was in? The website says that they offer an Associate Degree in Nursing (
http://www.sbcc.edu/nursing/adn/). If Cecile graduated in high school in 1978, it might not be possible for her to get a nursing degree in that time; the reason why I say this is because when my mother went to Long Beach City College to get an associates degree in nursing, it took her a couple of semesters to complete all of the prerequisites that she needed to enroll in the program and there was a waiting list to get in. She graduated in 1983 and took the state boards that summer. I don't know the specifics and I was really young at the time [thus, my memories are somewhat sketchy], so I could be wrong about Cecile Moch not having time to get a Nursing Degree in two years.
Was it ever disclosed why authorities believe that the unidentified woman was a nurse? Was the male found with her also believed to be involved in health care too? [sorry, this is one of the Southern California cases I'm not familiar with]