At the risk of sounding less than humble, I would say I was the best rebounder on the floor in the majority of the games I ever played. There was never any one way that I rebounded.
Put a body on whoever is close, then go after the ball with reckless abandon. Grabbed plenty of rebounds one-handed, but it was never a decision. Only instinct.
Also only fouled out twice in my life, both fouling late to stop the clock. Being the most aggressive rebounder on the floor doesn’t necessarily correlates with high foul rate, imo.
Being tentative is the killer, which is probably the point of saying go for the ball with two hands instead of one. Man thing is full commitment. If you feel like the ball belongs to you, it probably will. And the ref will agree.