The Library of Congress (LOC) does indeed store copies of many old-time radio shows. However, the Library does not the own of the shows. Any qualified person can access this material, or even get copies.
The process to obtain shows can be very long, frustrating and is Very Expensive
Noted OTR Researcher and writer, Elizabeth McLeod, who has done much research in the area, has outlined the process in Frequently Asked Questions (FAQ) File for OTR (Old-Time Radio.) See the below URL.
34. I keep reading/hearing about the LOC hoarding a bunch of unreleased OTR episodes. Is this true? How can I get them?
NOTE: that the LOC Audio Transfer Rates now costs over $110.00 per hour
ALSO NOTE: From Section 8 of FAQ 34:
Needless to say, you may not make any commercial use of the recording in whole or in part -- and you had to sign a contract to that effect in order to get access to it. Commercial permissions are a whole separate case.
Signing off for now,