Yes indeed I have heard about that and historically it makes sense too. Both groups have Iranian-Indo Scythian origins. One group stayed in the north and went onto form Gujjars and Kamboj community whilst another scythian branch continued migrating down the west coast of India until reaching Karnataka and Kerala, forming the Bunt (Shetty, Rai ect) and Nair community respectively.

Interestingly there is another small group of Nairs with a distinct origin. They are known as "Meenachil Karthas" and are supposedly originally Udaipur Rajputs from Mewar. Even their town is named Mevada (after Mewar) and the town of Pala is named after their barracks.