"Fighting through screens" is a foul. If a player sets a legal screen, and the on ball defender displaces him by barreling into him...that's a foul. The options are 1. Going under the screen and hoping you don't get burned by a three...or. 2. Switching and or hedging the screen and hoping your big can contain the dribbler or buy time until the primary defender can recover.
Respectfully, this is all incorrect.
You can't run the screener over, obviously, but you can absolutely fight through the screen (what some coaches call negotiate the screen) to dictate the guard being able to use it effectively and be able to recover quicker.
Also, the only 2 options are not switching or hedging. You can switch, soft hedge, hard hedge, flat, drop, red (double) or ice a ball screen, and those are just the main ones, there are other sub coverages within that plus some other, less-popular ways.
We do not switch ball screens by design, we ice side ball screens and we play a drop coverage on middle ball screens. When we switch, it's what's called a "forced" switch, basically saying that the guard did not do what they were supposed to do which forced the big to do a full switch, but it is absolutely not what we are schemed to do.
Because we ice the side ball screens, teams stopped doing that against us, they would run almost entirely middle ball screens because Oscar struggled so much in our drop coverage, and Toppin and Oscar were so good at icing screens on the side.