:::I don't think the claim is that Trent is not Tyrolean; rather, I think that while the region of Trentino-Alto Adige/Südtirol can properly be described as "southern Tyrol", with a lowercase "s", "South Tyrol" generally refers to the province created by Italy after WWI. This ngram shows that while "Tyrol" has been around for a long time, "South Tyrol" first appeared in numbers after WWI (the same is true, incidentally, for "Alto Adige", and "Südtirol". This view that "South Tyrol" is a modern invention is backed up here, among other sources.