PA is big enough that they're certain to take advantage of every opportunity to lower their tax obligations by claiming every expense possible. They would track all their expenses in their accounting and they'd have receipts or other records to show those expenses. Otherwise the friendly IRS would disallow those claims. If they failed to send the donated books, then there would be no receipt unless that was falsified. Either way, that would create a trail that would either lead to the person at the site receiving the donated books or to nowhere if the receipt was falsified. Out of the three possibilities, two are bad for PA.
However, if a PA author is smart, they'll have the donated books sent to them so the books won't be thrown out by the unsuspecting retailer but then that makes this offer no better than the two for one sales that PA was already doing. PA's merely throwing out a carrot that's no better than their previous claims by making it look like PA is willing to try to place books in retail stores.
By the way, many retailers have another way of dealing with unordered and unwanted merchandise. They refuse delivery and have the merchandise returned at the sender's expense. So even if PA does ship the donated books, many of those will end up back at PA's doorstep and then go into the trash. Net effect? PA pays twice for shipping along with the cost of the paper, ink, binding, and labor to produce the books. Then the books go into the trash since PA lived up to its promise to donate the books.
Also, unless the promise stated specifically that the book shipped would be that author's, it might even be some other books sent in its place that PA needed to dispose of.
