I'm not saying it's not, I haven't even looked up a definition, but I do know I've written firmware update code before... I think the way the term gets used is probably a little blurry...
My car, for instance, is a bit old. It has some sort of ARM device in it running a proprietary GPS system. There is an update mechanism that can be triggered when you put a new DVD full of map data into the drive in the trunk. This updates the stuff that runs the ICE as well as the GPS. I would be very concerned if it had anything to do with engine-control I suppose.
Essentially nothing like that is used anymore. Almost every programmable part is reprogrammable in-system unless someone takes extraordinary measures to prevent it from happening. That means that there is no longer any real distinction between "firmware" and "software," and there is no such thing as "read-only software," as you put it earlier. There is only "software" and "locked software."
This thread is all about who should own the keys to the lock.