TUR is an error, which I've already reported to Adobe. The correct Turkish language system tag is indeed TRK and, no, vendors should not use their own codes.
The presence of a Turkish language system tag in most of the Adobe 'standard' OT fonts is unnecessary, since these fonts do not contain the necessary diacritics for Turkish.
Language system tags are not currently utilised by any systems or apps, but they will be (probably first by Microsoft).