There is no California or Federal regulation that prevents an exempt employee from using a partial day of earned leave. An exempt employee can not use unpaid time of (leave without pay or LWOP) for partial day absences. That is because the employer can not deduct pay from an exempt employee for a partial day worked. They can, however, draw from that employee's sick or vacation time for a partial day absence.
Depending on the company's policy, that employee may be able to avoid using leave if their total hours for the week are equal to 40.
Edited to Add/Clarify: In direct answer to your question, for a partial day of work or a partial absence the employee should charge their company/get paid for the hours they actually worked. If you were using leave without pay for your day, the company can not dock your pay if you reported for a partial day. However, if you have earned leave, the company can dock your leave for the amount you did not work.
There is a difference between the employer expecting the employee to be on call versus the employee wanting and being available to work. If you are available for work, but there is no work or you couldn't get in due to natural disaster etc, they can't dock your pay.
If you choose to take vacation, but are expected to be on call, than you are not choosing to be available for work (you are choosing vacation). If you worked for 1 hour out of an 8 hour day because you were on call:
-If you had no earned leave, they can't dock your pay for the 7 hours you did not work
-If you have leave, they still can't dock your pay but can remove up to 7 hours of your leave for the hours you did not work