No, it is not just rings, it is numbers. Take rings out of the equation, look at Mason's playoff numbers vs Manu's. Same with Horry vs Manu. Then tell me who performs better.
Mason averaged 6.6 points and 1.6 rebounds and 1.8 assists this year in the PO. The year before he averaged 8 points, 1 rebound and 1 assist, while Manu averaged 18 points, 4 rebounds and 4 assist.
Manu did not even play this year in the playoffs and he was closer to Mason's numbers than Mason was to Manu in Mason's best year ever in the PO.