“We regret your loan application has been denied”

I received a letter today from a bank (a Fortune 500 company) based in Ohio, informing me of this. Amount of credit requested: $38,000 plus. The application was made through a Ford Mercury auto dealership in Michigan.

I looked up the bank online, and called its main customer service number. I told the representative the details. She transferred me to the loan dept. 

I explained what I had received, and told the loan dept. representative that someone had tried to impersonate me. I also told her “the loan application number and date of application are listed in the letter; would you like them?”

She demurred, telling me: “The letter was probably sent to the wrong address, and you can ignore it” .
I told her: “No; the letter contains my full name. Are you confident you are right, and should you seek advice on this matter?”

A pause; I heard her thinking. And while she was thinking, a rooster crowed in the background.