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I really dislike Credit One because of their fees and all their scam tactics. Honestly, I would prefer to get a secured card over them any day. Have you tried Discover's prequalify page? I've heard pretty good things with them.
Did the letter say "fraud alert" rather than "credit alert"? If that's the case, banks can pull your credit, but they can't approve you without additional steps to verify your identity. That would be the case with any card you applied for.
I agree with the suggestion above. If you can be approved by a different bank and let your Credit One application wither and die, you'll be better off. The hard pull would be a tiny price to pay to save yourself the headache of dealing with that bank.