Rama you had good information for the original question. Please see though that he did ask Pinnacle Group (I am assuming not just Pinnacle Airlines). Your clarification of who gets what travel benefits is appropriate.

Where this could be confusing is examples like Alaska Air Group. I work for Horizon but my travel benefits are for both Alaska Airlines and Horizon Air. Except that each is wholly owned by the Air Group so it is not necessarily a direct comparison to the other operations. Just showing where it might be confusing for someone not directly in the loop.