Stats alone don't prove anything, but they're a good indicator of performance.
Anomalies do happen though; I read that Modric only scored 3 goals and got 4 assists last season, though he's widely regarded as one of the best creative CMs in the league. Even Anderson got better goalscoring statistics than that last season, but does that mean he's better? No, of course it doesn't.
As I said, they're not a bad way of collating a players' overall performance if you don't have the time to watch them play all the time - but they're no substitute for actually watching and observing a whole game.