It could have been miss-delivered. One of the books that went lost en-route to me shows a delivery scan but I never received the book.  I checked with all my neighbors.  You could file a claim with the post office but I'm not sure anything could be done. If you bought postage through PBS then you got a credit and you aren't out anything. 

If you are worried that the receiver is a scammer, PBS will investigate an account with a high rate of lost books especially if there are multiple books showing delivery scans that are going lost.  But most likely they really didn't get the book.

Here's some additional info from the Help Center, but Mary covered most of it:

If you sent the book with Delivery Confirmation and it has been recorded as delivered by USPS but hasn't been marked received yet:

• Remember that the book could have been scanned as "delivered" at the local PO, before it went to the requestor's mailbox--the actual delivery can be a few days later  Also, the book could have been misdelivered.
  • The requestor should check with her mail carrier about this package.
  • The package could also be at her local PO being held for pickup; sometimes pickup notices left by the mail carrier go astray.
• You should FIRST contact the requestor using the button on the transaction on the Books I've Mailed tab in My Account when a few days have passed after delivery.
  • If the requestor does not respond to your PM within a week, or has not marked the book received by a week after the delivery scan (whichever is the later date), contact us.  We will look into it.
  • If the requestor responds and says she or he DID get the book, she or he can mark the book received one of two ways:
    • if the book has NOT been declared lost in the mail at PBS - from his or her active transactions (on the En Route to Me tab on My Account) as described in .
    • if the book HAS been declared lost in the mail at PBS - from his or her Transaction Archive (linked from the top of the My Account page)  as described in I received a book that was 'lost in the mail'.
• If you used DC purchased through PBS, or PBS Printed Postage, you will already have gotten your credit for sending the book.

If you sent the book with DC purchased elsewhere and it has been recorded as delivered by USPS but hasn't been marked received yet:

• First, contact the requestor from the active transaction (in the Books I've Mailed tab in My Account), or from the "lost" transaction in your Transaction Archive if the book has been declared Lost in the Mail by PBS.
• If the requestor does not respond to your PM within five days, contact us and we will look into it.
• We cannot grant credit for DC purchased outside PBS, but we can check if this requestor has become inactive.
• If this requestor is inactive, your book should be marked received by the system.

My post office usually marked a book as "delivered" when it gets to their post office ... and then it takes another day or two to actually get to me.

I once had a book scanned as delivered to me, and then it appeared in my mailbox 16 days later.

So, sometimes, the PO just messes up.

There are occasional Post Office errors.  If the book has not arrived by 48 hours after it was scanned 'delivered' it could be appropriate to contact your PO with the Tracking information.  They can sometimes locate a 'stalled' or misplaced item, but sooner can be better than later.
 

Some bit ago, I got a book offer and it got marked as having been delivered but I never received the book. I felt terrible because the sender probably thought I was lying through my teeth but I truly did not receive it. 2 weeks later, the silly book just showed up in the mailbox out of the blue (not damaged, no marks, not opened!). I was happy to pm the sender that it had arrived. I believe it had gone to the street over from us, which some gooniebird had been whacky enough to name close to our street name AND they have matching house numbers!! How silly is that??

I once got a book months after it was marked as delivered. It went lost in the system, and I got another copy, and then, it showed up in my mailbox with no explanation but with a postmark from months past. It was so odd. 

This just happened with me - the book was marked as delivered in April, but I only got it yesterday. I can't really explain why, but I was glad it wasn't lost in the mail.

If I put my mail on hold, then all my books are scanned as delivered when they are put in the hold bin.  Just not yet delivered to me.

My post office in my town tends to do really shoddy work. Multiple times books I have requested have already been marked as delivered by the post office but they don't actually show up in my mailbox until a few days later. I suspect that maybe they go out in the mail truck but then somehow don't actually make it into my mailbox. I'd say wait a few days when this happens and see if the book arrives later before taking action.

This same thing has just happened to me with an item I mailed on ebay.  According to the tracking information, the item was delivered on May 23, but the buyer messaged me, saying she hasn't received it yet.  I just told her to wait it out a few more days to see if it would reach her still.