Jim Brown didn't need stats to be good, he just out played everyone on the field for ten years. Barry Sanders didn't need a great line to be great, he just made everyone on the field miss once or twice a game for large chunks of yards. Walter Payton didn't need either and blended a little of both to be great.
All three have similar stats yet uniquely different traits, Barry was a finesse runner, Brown was a brute, Payton was a little of both. Stats only leave you with numbers to interpret and yes stats can be tied to team performances but so is greatness, the other half of the argument is the fact that these guys elevated their respective teams above and beyond what they would have been if an average player had taken their roster spot. All those players lead their teams in some capacity that was more than just tangibles.
To say using only stats is wrong, is as shortsighted as saying stats mean everything. Like anything in time you have to try and collect all the facts, weigh all the data (stats included) and reach a logical conclusion based on your findings. The likely hood of a player who amasses huge stats to be considered great is much higher than a guy with lesser stats simply due to the fact that numbers are a direct measure, leadership, poise, competitiveness etc...are traits and hard to quantify so by default play less into the arguments unless they are paired with stats.
To make a great player you have to have tangibles (stats and other measurable) and intangibles (leadership, elevation, competitiveness and other unmeasurable) and when you pair them both up you get greatness but only if you pair both up do you get greatness, you cannot be great with only tangibles and you cannot be great with only intangibles, it takes both to equal greatness.