You are correct. They did apply (orally) and you made a decision to deny their request. Therefore, you've received an application and an Adverse Action Notice is triggered.
The definition of an application is “...any oral or written request for an extension of credit that is made in accordance with the procedures established by a creditor for the type of credit requested.” [§1002.2(f)] It's not a piece of paper.
Reg B also states in the Commentary to §1002.2(f) #3:
"A creditor is encouraged to provide consumers with information about loan terms. However, if in giving information to the consumer the creditor also evaluates information about the consumer, decides to decline the request, and communicates this to the consumer, the creditor has treated the inquiry or prequalification request as an application and must then comply with the [adverse action] notification requirements under Section 1002.9. Whether the inquiry or prequalification request becomes an application depends on how the creditor responds to the consumer, not on what the consumer says or asks."
This example clearly demonstrates that an inquiry could lead to an application and a denial is triggered - as I mentioned in the webinar.