This is confusing authentication and authorization. Is this phone legitimately tied to this Apple ID? Yes. Is the owner of the account authorized to make such a purchase? No.
A short appstore PIN could solve this much more easily.
I'm not so sure having _yet another_ PIN for users to remember would be a good idea. And besides, a short PIN would be far easier to deduce by looking over a person's shoulder.
Yeah, it's configurable between "Demand my password again if 15 minutes has passed" and "Demand my password again immediately." You can tell you're going in the wrong direction when you first have to "enable restrictions" hoping to relax the restriction. I take it you've never actually tried to configure this option.
That said, it would be nice to have the option of telling the app to cache your credentials.