Centripetal Acceleration is always along the line of radius from the centre of rotation.
On a Flat Disk, like a merry-go-round, this will be toward the edge of the disk. On a rotating sphere, this will always be vertical to the surface of the Sphere.
So on a Rotating Round Earth, this centripetal acceleration would act to change the vertical vector of the thrown object. On a Flat Disk (like a merry-go-round), this will be towards the centre of the disk.
Thus, if an object is thrown on a disk, it is no longer attached to the rotation, and so is no longer being accelerated. The result is that it will move at a tangent from the point it was released.
So, Tom, you are wrong.