It even says on their website ( https://www.usbank.com/credit-cards/cash-plus-signature.html
If you do not qualify for the U.S. Bank Cash+ Visa Signature Card, you will automatically be considered for the U.S. Bank Cash Rewards Visa Card that earns 1% cash back on all net purchases, but does not offer the 5% and 2% Cash+ Categories or the $25 Cash+ Bonus once per calendar year.
They did say something similar on the phone.
However, the "U.S. Bank Cash Rewards Visa Card" is not what they sent me (I got the "FlexPerks Travel Rewards" card, which has an annual fee - big difference), and just because I will be "automatically be considered" for a card does not mean they are authorized to open an account for that card, because I never had the opportunity to review its T's and C's.
When I got the FlexPerks Travel Rewards card in the mail, the T's and C's said "you may still reject this Account, provided that you have not yet used it or paid a fee after receiving a billing statement". I'm hoping that this is their way of covering their ass, by offering you an alternative card that you can still "reject" before using it. Because I closed ("rejected"?) the account before using it, I'm hoping they will not report it as having been opened.
Has anyone seen any other cards that say in the T's and C's you can "reject" it upon receipt?