Re-visited this topic today. I actually think the ability to check the price of something using the Amazon app is a bit of a red herring. We already know that, in most instances, the item is going to cost less online.
What it really boils down to is comparison shopping. In the past, it was much more difficult for consumers to compare the cost of an item at different shops without actually travelling to all of those shops. But it was still possible for someone to check out a particular item (books, in this particular thread) at one shop, then buy it for less at another shop.
The main change is that now, with smartphones and wi-fi enabled tablets and iPods, the process is actually much easier.
And sometimes, it does work in favor of the brick-and-mortar retailer. I recently spotted a CD (101 Soul Anthems—a 5-disc set) at Half Price Books. Brand-new, and sealed. And an UK import. Unfortunately, their price sticker was affixed to the back, obscuring a chunk of the track listing (and, with the content of all 5 discs listed on the back, it was quite a chunk). So, I took out my iPod, and, thanks to the presence of the Starbucks next door, was able to access Amazon's web site so I could view the complete track listing.
Not only was I able to see the entire track listing, but I was also able to see Amazon's price. It was some $10 more.
Now, I didn't buy the CD just yet. The so-called Loudness Wars are still part of the music industry landscape, so I wanted to get some idea of what the thing sounded like. Even at the lower price, if the CDs had been unlistenable, I would have been disappointed, which would have made me less likely to decide to purchase similar items—from anybody—in the future.
Enter iTunes Music Store, which I logged onto when I got home. I had to switch to the UK store, but was able to listen to enough samples to discern that the audio hadn't been processed to death, so the bargain price for the 5-disc set would indeed be a bargain.
Next time I went to that Half Price Books, I bought a copy of the set. Meanwhile, Amazon is now offering that same set for $23 more than I paid for it at Half Price Books.
Now, admittedly, comparing prices for items sold at what is basically a thrift shop may not be a typical circumstance. But I mention it to point out that a price comparison between a brick-and-mortar shop and an online retailer is not automatically going to favor the online retailer. Sometimes the utility cost (the cost of having access to that item or service right now) is going to be low enough that the consumer will go ahead and pay extra to buy it at the brick-and-mortar shop. And sometimes the online price will actually be higher.