Credit Karma is not intimately aware of all of the underwriting guidelines at American Express. It's just a third party service that tracks credit. Its data roughly knows what people's credit looked like when they apply (because the inquiry will appear) then it knows if a card is issued (because the credit line will appear). From that Credit Karma has something resembling an estimated approval calculation, but it's not like anyone at Credit Karma sat down with an American Express underwriter to learn the ins and outs of specific approval.
With all of this in mind, why are you focused on that particular American Express card? There are plenty of other cards with great benefits and rewards programs.
Have you talked to American Express? Typically credit card companies have a reconsideration staff. Call American Express and have a chat. You might have too much available credit line compared to your stated income. They might just want you to confirm something in your credit report.
An anecdote for you. For my most recent Chase card I was soft-declined (we need more time to review your application), which I thought was very odd. So I called Chase and was asked a number of questions about my employment. While she didn't explicitly say it, I think the issue was that I listed my new employer and income number on my application. My new employer was never on a Chase application before and also wasn't previously on my credit report. These two nuances threw up a red flag such that they needed to talk to me before issuing the card.