It prohibits any outside employment whatsoever. It's not a conflict of interest issue, it's a "we're spending $100,000 a year training you and you will dedicate your time to just this" situation.
That sounds like crazy talk. Show us where in your contract it says you lose your funding if you take on any form of employment.
"Stipend and tuition fellowships are awarded to allow students to devote full time to the pursuit of a Ph.D. degree in the Training Program and to complete the requirements for the degree in as short a time as is consistent with adequate training and research progress. The student should not engage in additional employment while receiving a stipend through the graduate program, regardless of the source of that stipend, because such employment causes a serious impediment to the graduate educational process. Graduate education and research are of necessity largely self-motivated processes, and the distractions of outside employment can interfere with the ability of students to prepare satisfactorily for their future professional careers.
If additional income is necessary, students are encouraged to consider the possibility of low-interest student loans. Advice about such loans may be obtained from the University Financial Aid Office (listed in the Appendix section). If a student feels strongly that outside employment is necessary while in the Training Program, this must be discussed with the student’s Dissertation advisor and a formal request must be submitted to the Graduate Education Committee through the DGS. Students should be aware that such requests will rarely, if ever, be granted. However, if outside employment is necessary
and is approved by the Committee, the student must not allow it to interfere with high standards of performance and the timely completion of graduate education and research training."
So I guess it technically can happen, but it doesn't.