Goaltending, basket interference and the imaginary cylinder
Rules
Where the rim becomes untouchable, why a ball on the way down cannot be blocked, and the one case where it can.
Above the rim there is an imaginary cylinder, the same diameter as the hoop, extending upwards indefinitely. Once a shot enters that cylinder, nobody from either team may touch the ball. Touching it is basket interference, and the consequence depends on who did it: by the defence, the basket counts; by the offence, the shot is waved off and the ball goes the other way.
Goaltending is the related rule and it starts earlier. A shot that is on its downward flight and has a chance to go in may not be blocked, even well above the rim and well outside the cylinder. The moment the ball peaks and starts falling, it is protected. A defender who gets a hand on it after that point concedes the points regardless of how clean the contact looks.
The reason is practical. Without the rule, a tall enough player could simply stand under the basket and pluck every attempt out of the air, and the sport would stop being a sport. The downward-flight condition is the simplest line that prevents it while still allowing genuine blocks.
The exception people argue about is the shot that has no chance of going in. If a ball is falling but is clearly going to miss the rim and backboard entirely, it is not goaltending, because there was no shot to protect. Referees make that judgement in real time and it is among the harder calls in the game.
Touching the ball while it rests on the rim is basket interference by either team, as is touching the net or the rim itself in a way that affects the ball. A defender hanging on the rim as a shot arrives has given up the points. So has an offensive player who tips in his own teammate's attempt while the ball is still sitting on the iron, which is why you occasionally see a perfectly good-looking dunk cancelled.
Once a ball has hit the backboard above the rim on a shot attempt, it is still protected in professional rules until it clearly misses. Rules vary slightly between competitions on this point, which is worth knowing if you watch both international and US basketball and wonder why identical plays get different calls.