Think. Cars naturally lean THE WRONG WAY on curves. They tilt over toward the outside.
There's no "right way" or "wrong way" for a car to lean on a level surface with all four wheels on the ground. The motorcycle metaphor doesn't work well here because part of turning a two-wheeler involves moving the center of mass off the centerline and letting gravity pull you through the turn. To paraphrase Douglas Adams, turning a two-wheeler involves throwing yourself at the ground and missing.
This magnifies the centrifugal force you feel by adding a gravity component to it.
On the contrary: being thrown towards the outside of the turn means the turn radius increases, which results in a decrease in centrifugal force.
They tilt toward the inside, like a banking airplane.
Another poor comparison. Airplanes roll while turning because their wings are their largest working surface areas and need to be tilted off of horizontal to get the lift vector pointing "that way." The comparison here would be in banking the road surface itself (the working surface for a ground vehicle) rather than any shifting done by the suspension on a level road surface.