That radio was not burned. That is what they look like when they sit on the speaker foam in a parts box on a shelf in a garage for 30 years. That radio was not in a fire. The push buttons are sun baked and have gotten brittle. That is a '47-'50 truck radio. The slanted case and back cover with hammertone paint was used from '47-50 and then the silver metalic case with shoebox back cover was used from '51-'53. A little AD radio trivia for you there.
I have over 20 of these radios and I'd say at least half of all the ones I come across are missing the back cover. Typically, they would stop working and someone would pull them out and start tinkering with them and then invariably not get the radio working and the back cover would never get put back and would separated for the rest of eternity.
I have a recurring dream that some day, I'm going to go into a junkyard that has only suburban seats, panel truck tool box covers, radio back covers, panel truck passenger seats and a pile of other frequently missing parts.