Assuming a perfect sphere in a vacuum (pun? what pun?), the ball would deform perfectly by squishing in the direction of travel and expanding in all directions perpendicular to the direction of travel. The intersection of this shape with a plane is still circular.
Now, assume our perfect sphere is a ping pong ball, with a seam and variations in density along its surface. Further assume that our plane is made of wood with a variety of strengths, weaknesses and densities along its volume. And that said plane is also covered in a rough surface. The changes that these variations impart on the actual experiment leave a hole blasted in the paddle that's not perfect in anyway (see all those jagged edges?) But I believe it's safe to say that, with all these imperfections in all these materials, the circle is not a "perfectly ping-pong ball shaped hole," and certainly more difficult to measure than a perfect sphere slamming into a perfect plane.