Walt - while that sounds feasible, I don't think that is the case. It happened again today. I had over half a charge, about 23 mile EV range. I got on the freeway, and the ICE kicked on the same way I originally described. It would have run the whole way home, but I was pushing buttons trying to get it to turn off. At a light, I put it in HV mode. The blue line showed up and the engine shut off. I started moving slowly, still on electric, the top icon said Ready EV. I pressed the HV button to turn HV mode OFF (which should put me in pure EV mode, I've got plenty of battery). Instead of the blue line extending further, it disappeared and the engine turned on. I put HV mode back on, the blue line appeared and the engine shut off. The entire rest of my drive, when HV mode was on and I was hardly accelerating, Ready EV showed and the engine shut off. But every time I turned HV off, the blue line would turn all white, it would say Ready (no EV) and the engine would start up again. This was the case for my entire 15 minute drive home. When I stopped to park the engine was running, charging my battery. It burned very little gasoline, but my range on fuel came down a couple miles. I think I'll call the dealer and ask if there is some sort of software glitch they know about.
I cannot think of any reason, with over half a battery charge, that turning off HV mode should turn ON the engine under virtually no load, especially when the engine started out OFF in HV mode.