You need to consider if YOU have broadcast/synchronisation licence/permission to use the audio in question in the first place.  Basically if you do not have express (written) permission to use copyrighted material (and recordings of anything, even public domain music, are copyrighted to someone even if just to yourself if you performed them) then you cannot really demand the right to use it irrespective of the claimant's case (or not, as the case may be).