I had applied for the Amex product back in March, and tried this evening to apply for the Visa product. No instant approval.
Called the app status line, and the rep mentioned it had been denied due to already having an AAAdvantage card with them. She said they had been allowing people to have multiple cards, but had changed the rules today. Said it may change again in the future but for now, they are enforcing the rule again.
When asked if this failed the initial internal checks or a hard pull was done, she mentioned that unfortunately they had done a hard pull.