The propellor or the jet engine of an aircraft push air backwards to propel the aircraft forward. A ship or boat propellor does the same thing with water. On Earth there is always air or water available to push against.
You challenged the accuracy of the statement with respect to the actual physics of propellor-driven locomotion. As I read the statement to which you object, it simply states that propellor-driven locomation requires a medium in which the propellor can operate, and mentions that the principle of operation involves "pushing air backwards." The statment is incomplete, but is not incorrect (a propellor does in fact blow air in the reverse direction of the airplane, as anyone who stands behind the propellor can attest.) Of course, it would be incorrect to imagine that forward thrust derives in any way from blowing air against the air behind the plane (which is apparently how you interpret the statement at issue.)
Forward thrust results partially from conservation of momentum: by throwing air molecules backward, the propellor experiences a motive force in the opposite direction, as a consequence of Newton's Third Law of Motion. To me, "pushing air backward" is an acceptable way to state this, when one trusts that the audience understands the physics of motion. Although the pressure gradient created by the action of the propellor also contributes to the thrust vector, failure to mention this component of the thrust is not a sin in this context.
I enjoyed your explanation but I still have an argument with the statement above (not yours). It implies the force is derived from "pushing" against the air which is a popular misconception and totally ignores the fact that the air or water is accelerated by the propellor.
Are you saying momentum is not conserved and that the "pressure gradient" contributes but not in a way that conserves momentum? I think I will have to take issue with that.