That is all they do and can do. They confirm it works - but only if it's already running too ! If it's mid-January, in Ohio, an inspector won't turn on the AC or it's summer, they don't turn on the furnace. They get the age of the unit(s) and advise how many years it typically should have left. I'm making up numbers, but say the furnace is 8 years old and they typically last 15 years, they'll simply note it should be okay for another 7 years. That doesn't mean the blower motor, a circuit board, etc won't fail tomorrow though.
My neighbor is a home inspector and mentioned something that I was surprised about (related to turning on stuff): They will not plug things in to check if they work. Say a house is unoccupied and the previous owner left appliances but have unplugged them. He won't plug them in to see if they work. There is that very rare chance of a crazy fluke occurring and causing damage, either to the device or if it's already damaged, causing a problem with the home's wiring (even simply tripping a breaker).