You might as well be right. Actually, from what I gather, Turks are nothing but Uighurs, and Uighurs are the Ugrics, of the Finno-Ugric people. I have material to support this, but perhaps I will elaborate later.
Now, my guess is, Uighurs themselves are a mixture of Mongols and Finns. Now, as these Uighurs moved eastwards, along with the Finns (due to being kicked about by the Mongols), they went far, took their vocabulary, but largely assimilated with the locals. So, the further you go from East-Turkestan/Xinjiang, the less Turk these so called Turkic people are. By the time you reach Turkey, you are in Anatolia, the land of pseudo-Turks.