I think in the case of Özil in particular, who's one of the best players in the world without the ball, stats can highlight things that people overlook because their perspective is locked to where the camera points their television (which is usually the area of the pitch where the ball is). Even when you watch a game live you tend to focus on that small area of the pitch.
This is how we came to track things like key passes, for instance. People (sometimes) remember who played the pass when someone scores, but not when their teammates miss an attempt at goal either through pass or rebound. Key passes aren't flawless either, but it's a bulk statistic that adheres to the golden principle behind every sound analysis: it's more about quantity than quality... Whereas we tend to look for quality throughout a game. We register the assist and the goal. We don't store most of the broader picture.
The core of Löw's German revolution was based on pure time statistics. I heard him speak once about how they had brought down the time it took the average player to pass the ball again after receiving it to a world record 1.8 seconds. It was close to 3 seconds when he and Klinsmann took over the national team. In tight spaces where you fight for 10ths of a second, being quantifiably faster at releasing the ball than everyone else gives you an undeniable advantage. (This is something Arsenal are generally terrible at by the way, which is why you sometimes can feel the inertia through the screen when we pass the ball around. Again - finding the decisive pass that unlocks an early move or combination is another area where Özil excels compared to his teammates, and it's easy to overlook because some of our players have neither the touch nor the brain to exploit it).
Similarly, stats are useless without context. A good example is how the quicker centreback in any given pairing is usually the one who commits most defensive errors because he's asked to push up more often to intercept the ball early. Just like how the best players in the air sometimes have worse defensive statistics because they're asked to mark better opponents. Statistics can't tell you the quality of the opposition. They can only reveal the outcome.
I think the kinda outdated view that statistics aren't an important part of football stems from the misconception that people don't believe their own perception is biased. Which it is, of course. It ties into a broader question about how we perceive a subjective version of reality and how our brains are much worse at handling logic than most of us are aware of. In every neurological test that exists our rational ability has been shown up for what it is. People would do well to be careful when they advocate for their own ability to perceive what's in front of them.
