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Sorry, but this is incorrect.
Look at the video again.
Measure the height of the ball from the table.
Measure the height of the cup from the table.
Observe how the cup and the ball fall at the same rate.
The center of gravity of the board falls at the same rate, but it is also confined to the arc it traces out. The fact that the cup starts out slightly lower than the ball is indeed part of this problem.