Need tons more info, including type of policy (it sounds like a CGL). It seems more of a professional liability claim than CGL, but it could be both/either. One would need to look at the policy language, and the specifics of the claim to provide you with a more definitive answer.
As respects the exclusion you mention, you would need to look at it specifically, to determine what is defined by the endorsements terms. On first blush, however, it seems that the exclusion would not bar coverage.
You sent this under the heading of ROR, but was a ROR letter actually issued to the hospital?