That's still not stealing though.

That's a different argument. We went through this with VHS. If you tape a broadcast that you paid for, it is not copyright infringement. Unless, you start making several copies and distributing them. Recording a Netflix screen and keeping it neatly in your hard drive is not CI, nor stealing for that matter. The only leg they have to stand on is when people start making copies and charging for distributing it. But even that argument has always been dubious.