A computing system will compare various reference fingerprints each representing a reference media stream broadcast on a different respective known channel, and the computing system will determine that a plurality of the reference fingerprints match each other, thus defining a multi-match group of the matching reference fingerprints. Further, the computing system will determine that a query fingerprint representing a media stream being rendered by a media presentation device matches the multi-match group, thus raising a question of which channel is carrying the media stream that is being rendered by the media presentation device. By considering one or more attributes of the query fingerprint, the server may then disambiguate and thereby determine the channel at issue, and the server may in turn take channel-specific action.