The brief segment is available for those in the UK (and elsewhere?) at
http://www.bbc.co.uk/programmes/b006qps9 - 11 Nov's programme at 29:26-32:14, right after a segment on video game piracy.
It was in response to a programme last week when a listener said she didn't know what ereader to buy and was considering Kindle until she learned it can't be used to download from libraries (this is the UK, so no OverDrive).
"technically minded" listeners wrote in to say she could use a free piece of software called calibre (pronounced caliber

)
They called it free software by generous programmers; a powerful converting tool, but not pretty
They also said calibre was not really aimed at library books and libraries would prefer you didn't convert them because they keep track of costs/devices, etc. A bit confusing given that I imagine the library books here are locked with DRM so calibre - by itself - can't convert them. But I could be wrong as I haven't actually tried to borrow an ebook from the library - I think I might look into it to see how its handled.