Classical Music Library does have a free music download that is a promotional link to promote classical music. It appears front and center on the Classical Music Library web page. Every month the company gives free downloads to a music track that they select. That is the only free music download. If you start searching through the music and listening to the tracks, you will see that some tracks can be purchased for download. If you click on the the track to play it, you'll see a yellow icon appear under the download. Click on it and it opens a window that tells you the cost and how to buy it.
Naxos is a little different. The music tracks you listen to are still streaming from a database server but they provide a link to a website where you can buy the music. With Naxos you can use a static link from a track and link to it from another location. Here is one to try out: How's Your Mug?, http://cstcc.naxosmusiclibrary.com/stream.asp?s=41478%2Fcstccpaid04%2Fq69165%5F104
You'll need headphones.