This seems to almost sound like N-Tier application design.

Okay, here are my thoughts (as unimpressive as they may be):
Application Design and Information Architecture (which is what some people call web site design) are closely related, and then they aren't. Making a website an Application is almost a like asking to be hung, while designing a website with no Application focus can still get you somewhere.
The problem with a lot of newbies is that yes, they don't think of PHP as a programming language. This problem isn't because they are thinking of PHP as web pages, and not as an application, but because these newbies don't know how to program in the first place. I see a lot of PHP questions that aren't really PHP questions.
"How do I include a page?" is a PHP question.
"How do I include a different page depending on the link a person clicks?" is a programming question.
You can easily tell the difference in the questions: The former asks about syntax, the latter asks about logic.
Unfortunately, this is a problem that is difficult to fight against. You try telling a person who has been PHP scripting for 2 years that they don't know how to program. Programming isn't knowing a language well, it's knowing how to solve problems on your own.
For the most part, you will rarely see programmers asking questions on most boards and mailing lists like the above. Why? No, not because they know the answer. Heck, even experienced programmers from other languages who are just learning PHP follow the same pattern: Research the problem, search for the answer, solve it on your own. As you gain more experience in an area, you learn more and more. Programming is one of those fields where once you have learned how to program, the syntax is easy.
A person who doesn't know Java, but knows how to program, can probably read through the Java code easily enough, and make judgements based on experience. Similarily, a person who doesn't know PHP but wants to include different pages when a link is clicked can solve the problem without knowing PHP (Send a variable to the page, probably via the GET method, retrieve that value, validate it for security reasons, and then include the page). When they post a question (If the found the need to instead of finding the answer on their own), the question might look like this: "I want to include a different page depending on the link clicked. I thought about passing it via the URL and then including it based on the value of the link, any suggestions to this method, or other methods that work better?"
You should now be able to see the difference in the types of questions.
Now, back to the topic at hand: Whether web sites should be programmed as pages or programmed as applications.
The answer, if of course, both and neither. When developing a web site, you need to develop the application as you see fit. When the underlying code is being designed, each area needs to best fit the task.
For example, when I display the news on my front page of the website, I have simply included the code to do this in the page. However, other code, like comment code, is abstracted out into functions and included where I need it.
Tracking information is done as well, along with User information. I have includes all over the place. Certain other pages, like for tutorials, have the code included in just that one page.
So, in the end, knowing how to developing both styles will help you.