>> the superchargers take AC from the grid

> the charger delivers exactly what the car needs

You're both right. A Level 3 charger does deliver the right DC voltage the car needs, and it does so using power electronics that convert regular old grid AC into DC.

Level 1 & Level 2 charging: AC grid -> cable -> onboard charger converts to 400V DC -> battery

Level 3 charging: AC grid -> offboard charger converts to 400V DC -> cable -> battery

Same number of steps, same conversion efficiency. Tesla even goes a step further and uses the same hardware, building out the (low volume) Superchargers "simply" by ganging together a dozen (high volume) on-board charger modules and stacking them inside a weatherized outdoor cabinet. This commonality maximizes their economies of scale.