...little snip...Luckily my son had "purchased" the free iBooks app in 2010 and was able to download a working version to this iPad.
I do not understand the logic behind this, though. Why can't the same dialogue appear when I try to buy this item new, my son was asked whether he wanted to download a compatible version, it would seem quite simple to me all the components lready being there.
It's a function of the AppStore and Apple's business model. The offer to download an older version of the app is new with iOS 7. This was to prevent people not able to use apps - they had purchased - on older iOS versions after the app was updated for a newer iOS. The owner loses money if the app can't be used because a developer no longer supports the older iOS version. So, Apple made it possible to "rollback" the app version to one the buyer had before or that worked with older iOS versions.
Note that this doesn't apple to all apps (developers can tell Apple not to do this) and it can apply to all apps, to include the free ones.
This allowed developers to focus on the app running the best on the new iOS. Some developers, Apple being one of them, always update their apps to run only on the most current iOS. Most of the time, I believe it's because it's easier to maintain an app for the most current iOS - you don't have to worry about old code and iOS versions. It's cheaper to maintain just one version (and by maintain I mean to ensure there are no bugs or upgrading for more features).
So, people who paid for apps that are updated past the iOS they are running won't lose out. They can continue to download/install apps they've paid for/used in the past. They aren't just throwing their money away.
This was a big and welcome change. People no longer had to "throw away" apps that got updated past the iOS they were running. And yes, it was/is a big deal for those iPad1 owners, who can't go past iOS 5.1.1. The older version of the app may not have the latest and greatest features and updates, but at least they could install it on their devices - if they had it before the updates.
But access to the older versions goes out the window if you've never "owned" the app before. Owned being whether you installed it, paid or free. Since you did not own it in the past, there is no need to ensure it still works for you on your device and iOS version. You have no investment in it.
Again, this is a new process and is a welcome change. Before, people were SOL when apps got updated. While still not the best process, it's still better than getting left behind with a legacy system and losing your money.
So, since you never owned iBooks before (you never downloaded it under your AppleID), you can't get the older version. The only one available to you is the newest one and it runs on iOS 7.
And that long story is why you couldn't get the app but your son could. Hope it clarified things a bit and answered the question. Sorry for the ramble.
TL; DR: downloading older apps you had owned in the past is a marketing tool. It keeps legacy customers happy while encouraging new customers to upgrade to new iOS versions/iPads.