LEED management for multi-prime contractor project

We have a LEED 2009 institutional project with 12 prime contractors. There is a construction management entity with oversight of the 12 primes. This entity does not believe it can accept the role of the Div 1 required LEED AP LEED Coordinator, however it seems untenable to have 12 uncoordinated entities as several credits require documentation from multiple contractors. A specific concern of the CM is that they cannot receive documentation from the prime contractors and then post online themselves since they cannot attest to the information provided. Typically the prime posts and attests. We would appreciate any experience with a multi-prime contract that can address issues of LEED project management.