I think you're mis-informed.

Teslas can easily charge at other branded recharging stations; mostly you never see it as there is no point. The Tesla ones are good. There are adaptors to all / most public charging stations for cheap. I keep a few, and my wall-charger (for 120/220v outlets) in the front-trunk.

Non-Teslas charging at Tesla stations is new/not really a thing though.