In addition to all of the other very accurate comments here, I'll add one other thing:
While playing the game is almost definitely the best way to improve, there are other ways to get better at league as well.
Someone who's played more games versus someone who's memorized every champion's cooldowns for example would be tough to determine the better player. All else equal aside from those two points, the former player probably has better mechanics, map awareness, and decision making. The latter player probably is better at choosing when to trade in lane, when to force fights, etc... The net effect could go either way depending on the relative importance of each factor and the difference in ability in each factor.
I admit the above was not the best example, but admittedly it is hard to come up with ways to get better at League outside of actually playing. Spectating may make you a bit better, but it's really nothing in comparison to playing...
I agree majorly with the idea that someone playing with the attitude of learning will be much better than someone who's played more games but plays with the attitude that they're already the best.