I think that rule specifically applies only to multiple apps sold by the same developer. The app in question is going to be offered by each company as their own, meaning each copy will appear under a different company's name.
So it's definitely allowed, but is it possible? Yes, but it might be a little tricky. I'd recommend that you create a custom framework that basically encapsulates the entire app, but without any branding. You can either give the framework to the client and let them add the branding and then export the app and all that, or you can create multiple projects with different branding, based on that framework, and give those to the clients. (I recommend the first option.) With a setup like this, you can modify the code in one place (the framework) and all of the cookie-cutter apps will get the update.