This is mostly correct but I am trying not to get too complicated with the explanations. What you left out as a factor though is how dirty the balls are, which is probably the most significant factor of all. You also left out what amount of english is used (a quarter tip or two tips etc) not just the type. Keeping it as simple as possible though, for the vast majority of balls frozen to the rail, it is best to hit slightly rail first. Your subconscious will learn to do what it needs to over time for all situations, but if you needed to think about it just one way on a conscious level while learning, this would be the best one--slightly rail first.
https://www.youtube.com/watch?v=_taEBDVQBYQ