To expand on this for the OP, the point here is that the commentary to Regulation B explains that when you have enough information to deny a loan, the request becomes an application by definition of Regulation B. In other words, you can't fully rely on TRID's definition of application when it comes to denials.
The commentary you refer to, Adam, tells us that the application becomes a
completed application on denial (since we had enough information to make the denial decision), and the fact that the application has become a completed application starts the clock on the 30 days within which the Notice of Action Taken, etc., must be given. It has nothing to do with the notice required by §1002.14(b).
The requirement for the notice to an applicant for credit that is to be secured by a first lien on a dwelling is not dependent on the application being a completed application. It is triggered simply on receipt of an application for such credit, long before it becomes a completed application. And 1002.14(b)(4) clearly says the notice is required whether credit is extended or denied,
or whether the application is incomplete or withdrawn.
As I have suggested many times, it does fly in the face of reason to require the notice if the application is denied or withdrawn within 3 business days of when it was received (before the notice has to be sent). But, as I have also suggested many times, it is easier to just provide the notice than to waste time looking for reasons not to.