I am sure thousands of amish would give oil swishing a try, they are suckers for anything on paper, it seems they believe most of what is put on paper, they have problems not trusting people.
Mixing salvia with oil in the mouth does not make any sense and much if not all of the Ayurvedic stuff makes about as much sense. Most of it is not harmful and anything written about enough lures many to give it a try. Maybe 10 years ago I may have tried it, but not that nieve anymore.