I agree that it all sounds a bit strange so here's my $0.02 worth (is that groans that I hear?)

Is the engine mounted sideways or inverted?
If it's mounted sideways - it may be that washer adjustment is simply altering the carb height in relation to the tank - just enough to help it idle at low tank pressures.

Otherwise
Either it is very rich at idle as Not24 has alluded to

or
the engine mount is somehow placing uneven strain on the crank case via the engine mounts (I don't know what plane or mount is involved here). this may cause some warpage as the engine heats up and may cause some sort of leakage that is affecting the idle (I know that they don't aspirate through the crankcase but who knows what happens sometimes).

Or
It suffers from the bumble bee syndrome - (nobody told the bumble bee that it can't fly - so it flys) It's the power of persuasion and positive thinking. - Either way it's always good when something works.