Took one of the machines to the local outdoor power equipment shop and the mechanic told me that crappy, low octane gas was the culprit. He said low octane gas with ethanol can actually cause air cooled motors to run hotter than they should and they'll just burn up prematurely. His suggestion was to use gas with a minimum octane of 89 and to only use premium two stroke oil with a fuel stablizer in it.
I think your mechanic gave you only partially correct advice. An older motor jetted for alcohol free gas will run a little leaner with alcohol blended in. That will cause the motor to run a little hotter, possibly even enough to damage it when combined with fuel passages that are restricted by varnish and such, making the lean condition even worse.
I don't know for sure but I would expect more recent motors to run an air fuel ratio that already accounts for the alcohol content.
As far as I know, the octane rating does not make your engine run hotter or cooler. It makes your fuel ignite at a higher temperature, which helps prevent detonation from a hot spot on the piston top or something like that. So higher octane could help in that regard if your air fuel ratio is overly lean.
But just blindly telling you to always run 89 octane or higher isn't very good advice, in my opinion. If you buy a new gasoline powered tool and the manufacturer says 87 octane is OK, you can be pretty sure they have considered the fact that pretty much everybody is going to be running gas with alcohol. So buying higher octane gas than your tool calls for is just a waste of money in most cases. Same with your car, by the way.