If that were true, roll-off wouldn't happen. Roll-off does happen. It doesn't matter whether the force to the side is from Fat Fred standing too close or the fact that the table leans west or that there's a nice spring breeze through the window. You do a sum of forces and that tells you which direction the ball will be accelerated in. This is very basic physics.I'm saying that any potential gravity effect from the body will be negated by the friction of the cloth preventing any sideways motion. I believe there is a small depression in the cloth created at the ball/cloth contact point and this will prevent that table roll effect...
Thick cloth does hide table tilt, but that's because the ball doesn't roll for as long on slow cloth. The longer the ball is rolling, the more time the small sideways forces have to act.