I moved mine laying flat on its back and had no issue. Let it sit for days before plugging it in.
It's not when things work well that count the most; it's when they go wrong and could have been avoided.
Remember that we're discussing old, probably well-used units here. New systems tend to be cleaner inside when built, have different bearing materials, tighter clearances, and modern improved insulation on the wiring. They also don't have significant wear on any of those components.
Not only can oil get into the cap tube system and cause high pressures, but moving the compressor on its side stirs up the sediment too, and if that ends up getting into the compressor (by later settling elsewhere than the bottom), it can plug the system for good. Also, springs from those days don't have the fatigue strength and cycling ability modern alloys do, so the old, used suspension components Greg discussed, besides coming apart, can also break more easily than modern ones. I wouldn't tempt fate, if not unavoidable.