High octane and lawn mowers

I had a colleague who owned a VW van–air cooled four cylinder engine. He bought the Clark gasoline we used to have in the area–all gasoline was premium at a regular price. He had to have valve work done because of some burned valves and the mechanic claimed that it was due to the high octane gasoline in an air cooled and that he wouldn’t have burned the valves with low octane gasoline.
I thought that this was bull, so, in the interest of science, I ran my lawnmower on high octane gasoline (I also thought I wanted to get a new mower that was self propelled). Well, the engine still runs and I have had the lawnmower since 1988. Even though Ben Franklin says “A penny saved is a penny earned”, I don’t think over the summer season that you will go bankrupt using premium in your lawnmower. The lawnmower doesn’t really need premium, but if it is convenient, that is what I would do.