Why can a two-cycle engine be run in any position?

Actually several reasons: 1. Because it doesn't have an oil sump for the crankcase; the crankshaft and connecting rod are lubricated by incoming fuel, which must be mixed with oil. This is part of the basic two-cycle setup, which if not understood would be a question of its own. 2. Because the fuel is supplied to the engine via a flexible drop-tube in the gas tank; the intake end always falls to the "bottom" of the tank, no matter which way it's held. 3. Because the two-cycle engine has no carburetor, thus no float which would otherwise prevent off-axis operation.