A UCM ad-hoc conference is a hub-and-spoke topology, with each endpoint having a separate active call into a central conferencing resource. Therefore CDRs from each endpoint to the bridge device reflect what happened and are valid from that perspective.
These phone->bridge CDRs contain unique information that is needed to model/interpret the actual call legs that were created during the scenario.
Additional discussion, including a scenario walkthrough with detailed CDR data is available in the CDR Admin Guide:
http://developer.cisco.com/web/sxml/docs