Holy crap, I think that is where I heard of it, and not a more authoratative source.
For a year or so, back in the '90s, I was a volunteer reader with Chicagoland Radio Information Service, which provided a similar sort of service, but we read newspaper and magazine articles over the air. We’d do a one-or-two hour shift; depending on the time slot, we might be reading articles from the Chicago Tribune, Newsweek, etc. (One of my fellow volunteers told me that he loved working the time slot where they would read the comics section; he’d describe the visuals in each strip as well as the dialogue.)
At the time, our listeners had to use a special radio to listen to the broadcasts. Today, while those radios still exist, one can also listen online, or through a smartphone app.
That link mentions Cecil saying it. I couldn’t find the actual column itself-- It might have gotten lost in some site update or migration.
Yes, the program is administered through libraries and not the internet for the simple reason that it predates the internet by decades. (Wikipedia says the Books for the Blind program started in 1931, first with books in Braille and shortly thereafter audio books.)
And my guess is the books could be provided via the postal service so no travel is necessary.
This is what my mother had as well. The NLS is the federal service that provides these things at no cost to the user.
My mom had her account set up so that once she returned a set of tapes, new ones would be mailed to her.