> Previously, couldn't cops just claim you were interfering regardless of distance or number of warnings?

They can still do that, too. Interfering is still illegal no matter what you're doing or where you are when you do it. Simply filming is protected by the first amendment, so unless you were doing something else you had a defense to say you weren't interfering. Now that defense is gone. It doesn't matter whether you're actually interfering or not, now you can be arrested and charged for simply filming.