I am aware of the vague language in the policy about the employee OR employer can terminate employment at any time without advanced notice or with any explanation.
There are so many labor laws and human resource laws in California that I'm suspicious that this is not all forthcoming. Is it really that simple? Can I really terminate my employment without an explanation and have no issues? (Leaving out that I am not looking for a reference.)
Yes, you are free to leave at any time. The most relevant law pertaining to this issue is the 13th amendment to the Constitution which prohibits slavery.
The only time you could really have any issues would be if you were contractually obligated to work for a certain period of time and you had already been paid for your work. A common example would be if your employer agreed to pay off your student loans provided you work there for 2 years. If you leave before these two years are up you may have to pay back a portion of the money. Other than that, you're free to leave.