I don't know what this brings to the debate (I'm kind of lost as to what's being debated anymore, honestly), but here goes...
1. A lot of these cleaners have abrasives mixed in. I've got about 20 different bottles here in the room with me, many of them already named in this thread. You can put some of these on your fingers, rub them together, and they feel like face cream. But others, you can rub them between your fingers and it feels sandy/chalky. You don't need a chemistry degree to tell you why. If you want to double-check this for accuracy, use the product on something that has no oil in it -- like the surface of your car. Many of these cleaners operate similarly to car wax; i.e., buff it out enough and you can shine painted metal with them.
2. Another way to check this: Get a bunch of rags, put various cleaners on them, then put them somewhere and let them dry out thoroughly. Like, 2 weeks. Then take the rags and shake them/pop them vigorously. You'll see dust fly out of some of the rags but not others. Know what that dust is? Yep, it's a sanding/polishing compound that was present in the original mixture.
3. The oil coming out of your bowling ball is actually EPA-regulated. I have been told, but do not know for sure, that it is mineral oil. Reason being, the oil gets everywhere, on your clothes and your hands, no matter how careful you are with it, so it has to be something very safe for human contact and also very easy to break down/remove. Figure out whether isopropyl alcohol will cut mineral oil and you'll have your answer as to whether it's a good cleaner.
4. As for how certain cleaners "draw out" more oil, there's really only two ways that can happen. One, the cleaner could have a surface-affecting compound in it, and rubbing this substance across the ball would actually cut into the sides of the pores somewhat and help release the oil. I suspect this is the science behind cleaners that are not approved for use during competition, as they would be modifying the surface of the ball itself, even if only by a minor amount. Two, a cleaner could chemically latch on to the oil molecules and pull them from the pores. If this is the case, it is certainly plausible for specific cleaners to be more adept at cleaning a ball than alcohol, which to my knowledge won't bind to mineral oil.
Jess