TPs are an internal BA mechanism for determining status. AA simply reports what you flew and the circumstances. Thus, AA will report to BA, in some odd code, that you were downgraded and refunded as you are entitled under the COC.
You are certainly free to make the ORC request to BA, but expect to be denied absent someone at BAEC erroneously entering the credit or expect BAEC to reverse the additional credit if the ORC is audited later.