I don t think the claim is that Trent is not Tyrolean rather I think that while the region of Trentino Alto Adige S dtirol 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 S dtirol This view that South Tyrol is a modern invention is backed up here among other sources