You are correct on both points.
However, destroying the whole hard drive is not essential. Opening the case and destroying only the disks is all that is required but the fire has to be REALLY hot to burn the disks. They are metal.
A data recovery company somewhere in the DC area recovered data from a hard drive that had been severely burned in an office fire.
When I replace my hard drives I take apart the old ones and remove the actual metal disks. I then use a pair of long handle needle nose pliers to hold each disk and melt it with a MAP gas torch.