OK, I just ran my MEP-003A. First I disconnected the output of the main transistor at terminal 17 of the regulator board. This terminal sinks the current through the exciter field control transformer CVT1 supplied from terminal 14, which is in turn supplied by rectifying diodes CR6 and CR7 (maybe CR8 and CR9 in some boards), which are supplied AC by T1. I connected a Fluke 87 meter between wire X39C16 and terminal 17 so that it reconnected the wire and read the current that the main output transistor was carrying.
Then I started the generator as usual, running at 1800 RPM. The current was about 230 mA to keep the output at 240 Volts. Then I reduced the engine speed with the governor cable as low as it would go. This really isn't what I'd call idle speed, but it's considerably slower than 1800 RPM. The current went down to 130 mA. After letting it run like this for a couple minutes, I stopped the engine and felt Q3, which is the big transistor on the board. It was about the temperature of everything else in the control box... cold.
This is not a recommendation that everyone go out and idle his MEP-002A or MEP-003A. I do hope it provides some information and dispels a myth. As I said above, there may be other reasons that it's not good, or even bad, to idle these generators, but so far all I've thought of is that it wouldn't be good to do it while a load is connected.
Also, as I said above, only the MEP-002A's -12 "OPERATOR AND ORGANIZATIONAL MAINTENANCE MANUAL" has the warning against idling, the MEP-003A's comparable manual does not.
I have no doubt that Q3 sometimes fails, and I'm sure that's not the only component on the board that does, but at this point, I do not believe that Q3 or anything else in the regulator will be damaged, or even stressed, by idling.