Apart from a few idiots nobody claims it is Turkish dialect.

There are some shared vocabulary, but thats pretty much it. Kurdish is much closer to Farsi.

Instead of parsing "mountain Turkish" as "mountain+turkish", parse it as " mountain turk+ish". The use of the term "Mountain Turk" arose in the Atatürk era as a quick way to nip any discussions of those ethnic minorities in the bud. That is all the term serves for. It doesn't mean that Turks believe Kurds actually speak a language genetically related to their own.