I tend to agree - my impression was that the agent was making things up to get rid of me. Her initial "explanation" was that I did not get the card because I canceled the application when seeing the no-welcome-offer popup (no duh). However, my real conclusion was that (a) you can't get around this by applying over the phone, and (b) no one at Amex is going to tell you why you're getting rejected.
I saw some data points from r/churning suggesting that a few weeks of regular transactions on your existing accounts may get around this, so I think I'll put some daily charges on my currently sock-drawered Blue Cash cards and see if it helps.