COBRA for school plans

Hello,

I wanted to ask about my rights under COBRA. I am currently a graduate student in a university in California, and my health insurance is offered through the university (they pay most of the premium). I was told that my plan is a group plan, hence I assumed I would be covered under COBRA upon graduation. But upon consulting the agent at the health insurance, they made a difference between school group plans and employer group plans and told me that COBRA does not apply under school group plans.

I am truly confused by this, as everything that I read about COBRA seems to apply to *group* plans, and they do not make a distinction whether it is school or employer. I anyone knows whether school group plans are exempt from COBRA and can point me to the source I would be very appreciative. Thanks!  

P.S. 1 – The source I am looking at is the following: https://uscode.house.gov/view.xhtml?req=(title:29%20section:1191b%20edition:prelim)

which defines group health plan as:

The term “group health plan” means an employee welfare benefit plan to the extent that the plan provides medical care (as defined in paragraph (2) and including items and services paid for as medical care) to employees or their dependents (as defined under the terms of the plan) directly or through insurance, reimbursement, or otherwise. Such term shall not include any qualified small employer health reimbursement arrangement (as defined in section 9831(d)(2) of title 26).

P.S. 2- As a graduate student the university pays me a stipend for research and teaching assistantship. I am not staff, but am I student-employee? In case that helps elucidate this case.