American Express had travelers checks long before it had its first credit or charge card.

American Express Bluebird is not a credit card, it's an online checking/debit/billpay account.

It has online banking too:

https://www.discover.com/online-banking/

And Discover constantly sends me invites to use their Savings Account. Not to you???

They also do home loans.

(The Discover card started at Sears, though now Discover Financial Services is an independent company.)

Just because they don't have storefront banks everywhere like Chase and Citi does not mean they're not banks. They may have a larger percentage of their business be credit cards than other banks, but they're still essentially banks.

Anyway, the main point here is that these are companies for which credit cards are just a part of their business. One you realize they're banks, how likely is it that a bank would want to buy an airline's FFP program???