The problem with gensets running unloaded for long periods of time has to do with building up deposits in the engine, nothing to do with the generator portion other than the only way to put a load on a genset engine is to have a load on the generator. That's why some large standby gensets have "exercisers" that connect it to a load bank so they can simulate a load and prevent that deposit formation. On smaller ones it's usually easier to just run your load from the generator a couple times a year.
The myth on the unloaded motor vs counter emf issue is something I heard a long time ago too. I think it's a misinterpretation of basic motor theory. When a motor is first connected to a power source and it is not turning, the only thing restricting current flow is the wire resistance, which is so low that the initial inrush can be 10-20x the FLC and it that went on for more than a few cycles it would damage the motor. But the instant the motor starts turning, the counter emf begins to impede the flow. So I think someone misinterpreted "not moving" with "unloaded" and fostered that myth.