They are using a straight shot, you push a rod with the sideways squeegee part attatched into your barrel all the way to the back of it, then you pull on a lever, etc. which straightens out to fit your barrel's diameter completely. Then you just pull it out, bringing the paint with it.
I'm sure someone can explain it better than that, but there 'tis.
if you break a ball in your barrel (which is the only time most pros break because high end guns have eyes) then the shells will usually come out and you will be fine. But if you break a ball in your breech and the shell or ball doesn't come out them you have to take off your barrel
You can also figure out how far down you can push the squeegee without hitting paint currently in the breech. That is almost as good as taking off the barrel. If it's worse than that, even taking the barrel off probably won't help much (it's probably messed up in the breech, the feed tube, and/or the hopper). Just shooting 5 to 10 shots might clear it up, but it might not. Better to do a quick brush without popping any paint.