Okay let's go through the scenarios, I'm pretty sure these are correct:
1. White ball hits rail before any other ball. It then hits a contact ball and neither ball hits the rail = FOUL
2. White ball hits the rail before any other ball. It then hits a contact ball. If the white or the ball contacted hits the rail after that = LEGAL SHOT
3. White doesn't make contact with the rail but hits another ball that does. LEGAL SHOT
4. White hits a ball which doesn't hit the rail. White bounces off this ball and hits the rail afer hitting the original ball = LEGAL SHOT
In basic terms at least 1 ball has to hit the rail
after
contact has been made between the white ball and the ball that was initially contacted. It's obvious but I guess it needs saying that this doesn't apply to snooker at all. It also doesn't apply to the 9/8 ball break shot where a certain number of balls have to hit the rail in total (4 I think :).)
The rule seems consistent to me, I've never had any problems with it. I've never seen what you explained (white ball hits rail - hits another ball - neither hits the rail - shot is allowed) so can only assume you didn't understand what happened fully.