Not sure about the earlier models, but my 54, while not having a radio, did have a black square of a cardboardy material behind the speaker grilles that hid the underdash stuff.
This sounds like the same sort of mesh that Brad was talking about. Mine was not a cloth material however.
I dont have it on hand to look at but if memory serves it was about 5"x5" and about an 1/8th inch thick. I know I read about it somewere, believe it also served to hide the speaker from view through the dash grill.
As was also mentioned the solid parts of the grill bar on either side of the open ones were painted black on my truck, as were the bars on the ash tray.
Hope that helps
Chooglin