Whether a load can push the motor rather than the other way around isn't a side detail — it decides if you need a brake, whether the joint is safe to touch, and whether it holds position with the power off.
A backdrivable mechanism is one where force applied at the output (the load side) can drive the mechanism backward and turn the motor shaft. A non-backdrivable mechanism is one where output-side force, no matter how large, cannot turn the motor — the mechanism physically locks against back-driving. This single mechanical property, which is a function of gear geometry and friction rather than of the motor or controller at all, determines whether a joint feels alive and compliant in your hand or feels like it's bolted to the wall, and whether removing power leaves an axis free to fall or frozen exactly where it stopped.