To me, a painted wooden radio is a red flag that the cabinet underneath had severe finish damage which the "restorer" did not want to deal with. For example, in the late 30s-early 40s many radio manufacturers (most notably, Zenith) fell in love with photofinished appliques to simulate expensive woodgrain. These sets are stunning when they are in pristine condition. But anyone who has seen one of these sets that has been knocked about will know how horrible they look when the finish is scratched. Worse, it is really not possible to restore them to factory condition since the factory bookmatched grain-pattern appliques haven't been made for many decades. Since the woodgrain decals are applied directly to unfigured softwood, removing the appliques and staining what's under them doesn't give a nice result, either. So, many of these sets end up being painted.
I'm not sure that that is such a bad fate for these radios if it keeps them from being scrapped out. Maybe in the future some radio entrepreneur will start to manufacture copies of the original woodgrain appliques, and these still-intact but painted sets can then be stripped and restored to their original glory.
http://www.radioatticarchives.com/radio.htm?radio=6883