I'm aware of the US system and how it works, but it has a lot of stuff that simply wouldn't pass muster here ('suicide cords' being only one of them)
The 'neutral/earth' has to come from the generator, if it was truly only a earth and two lines as you said before (actives as we would call them here in Oz) then if you had no loads between the L2 and the neutral line, any connected loads on the L1/N circuit would have their N floating, and wouldn't work... and connecting a load on the L2 would then provide a path from L1 to L2, with the voltage on each depending on each loads apparent load resistance...
Not good, as you could end up with well overvoltaged on one half, and undervolts on the other half....
'Smokin' as the Mask likes to say...
(the combined earth/neutral hasn't been allowed in new installs for several decades here in Australia (1970's/80's from memory) and if you used the same breaker system as in the UK or Oz, a 'suicide cord' like that genny/drier one wouldn't work anyway, as you would be using the earth circuit as part of the current return path, and the protection MCB's would immediately trip)