If you look on eBay or other sites, you’ll see that people stick the label public domain on virtually everything they sell, including old television shows and movies in addition to radio.
The copyright question is murky as to the originals in the same way that newspaper copyrights are murky. In the past, there was no expectation that material once broadcast would ever or physically could ever be used a second time. A few means of transcription existed - large platter records for radio shows that could be replayed for armed services radio or kinescopes, literal movies made by photographing tv screens, e.g. However, there was no commercial market for these, no consumer market for these, and no belief that anyone outside of a few insiders would ever encounter them. Newspapers were similarly transient. Important and unique stories were copyrighted so that they could be resold with credit to others. These were so few and so special that the fact of a copyright was trumpeted as part of the story. Most newspapers, however, were one time use only. With no expectation that the words would ever be used again, there was no reason to go to the daily expense of registering a copyright. Automatic copyright upon print or broadcast did not exist either.
It’s not clear to me, although others would be more expert in this, whether the Library of Congress kept good records of copyrights of individual radio or television broadcasts. If they did then the original copyright should be searchable. Renewals of copyright were not as well documented, even by the LoC, however, which has lead to much confusion. You can pay to have the LoC staff do a copyright search for you, which made sense before Internet databases were developed and if you had one or two specific items to search. I did that when I was editing an anthology. But nobody who makes hundreds of programs available for free could afford this service.
I think the rule of thumb presumption today is that most early radio and tv shows were not originally copyrighted, but that movies were. But I have no way of knowing whether any individual or particular show was copyright, was renewed properly, or is still in copyright. I’m sure that some of the sellers are simply lying about their claims of public domain, some are sincere in their rule of thumb understanding of the situation, and some have done the necessary research. But I couldn’t tell one from the other if I tried.
Some download sites are obviously done by knowledgeable fans who probably know way more about the subject than I do. If you can find what appears to be a good trustworthy site that pays attention to the problem, then I’d go ahead. But I’d beware of buying CDs peddled on eBay or other pay sites unless you know the sellers or the programs very well.
There are bills being introduced in Congress to handle the problem of orphan copyrights. Today the law is simple and straightforward: a piece that can be called an orphan is still under copyright. Period. There is no legal apparatus for using these works without infringement.