I don't know, but with a direct-drive diesel, you either have the engine (and prop) turning, or you don't, and there's a minimum forward speed, you can't just "idle" as I understand it. So I don't know if running dead slow ahead would've helped or hurt, if the anchor was already holding all right. It might have increased yawing if it put slack in the chain(s).
I'll defer to others with bigger licenses, but to requote something I heard long ago, "When there's a casualty at sea, there are many wise men on shore". I'm just wary of the tendency of this "wisdom" resulting in hasty criminal charges.