In Rails, the application belongs in app/, not lib/ or a gem. If this does not meet your admittedly obsessive design concerns then I suggest not using Rails.
You do understand that when the author says "your app" what is meant is "the domain or business logic that drives decisions."
Seriously, what's with the attitude? There's more than one way to architect software and Rails doesn't cover every single base. Pulling business logic out of your ActiveRecord models and into separate classes makes it easier to test and easier to manage code that interacts with more than one model.