Sure sounds like you are on the right track. A fuel starved 2 cycle engine is not good. When it runs out of fuel it leans out and can cause damage to cylinder or piston. That applies to any 2 stroke that runs on mixture, chain saws and weed whips also. If oil injected maybe not a problem. The 2 Stihl dealers near me say that 90% of chain saws that have cylinder damage have been run out of fuel.