The Rotary International Code of Policies appears to require clubs to maintain appropriate liability insurance. 

Correct

However, I have been unable to locate any Rotary International policy that specifically requires clubs to use AON or prohibits them from obtaining equivalent insurance elsewhere.

The renewal material states:

"AON is our appointed broker for the whole of Zone 8"

and

"Rotary organisations included in this program cannot opt out and appoint another broker."

ZIPC is a committee of Zone 8.  Zones (planned to be come regions) are and administrative and report layer instantiated by Rotary International with Rules directly overseen and approved by Rotary International.

On the issue of broker appointment the Rules include this provision:

7.6.2 Responsibilities Its responsibilities are to:

7.6.2.1 negotiate with insurance companies and brokers the most cost effective common insurance cover for Rotary activities carried out by clubs in t h e Z o n e as listed in rule 7.7.2.1.3 below (the Scheme) and advise incoming governors of 7.6.2.1.1 within reasonable commercial in confidence limits, the process, course and outcome of the renewal negotiations for the Scheme for the coming year;

7.6.2.1.2 the cost, terms and conditions, extent and level of the cover available for the coming year with an emphasis on changes from the earlier cover;