Yes, BLDC is a synchronous AC machine, usually operated with encoder feedback. I agree that the term BLDC is misleading, but it's somehow established. For small BLDC, e.g. fan motors with built-in electronics, the term describes the user view on the motor which has just two DC supply wires. But larger BLDC can't be distinguished from regular PM excited synchronous machines with or without sensor feedback.BLDC sounds like DC, but in fact it is similar to an AC synchronous motor. BLDC needs a lot power control circuit.