Does the water that flowed onto the hand become musta'mal (previously used) and impure, and thus invalid for ablution, if I took water in my palm to wash my hands up to the elbows during ablution, then raised my palm and the water flowed onto my hand?

What you heard is incorrect. The water you mentioned is not considered "used water" (ma' musta'mal) in the terminology of jurists, and its use is not disliked. The "used water" that jurists discussed the ruling of is the water that separates from the limbs of one performing ablution (wudu') or ritual bath (ghusl). Therefore, water passing over a part of a washed limb does not make it "used water."

"Used water" is pure (tahir). The disagreement is only whether it is pure and purifying (tahoor), or pure but not purifying (ghayr tahoor).