If you have no collections or public records then there's no reason your scores should be in the lower end of 600's. So that doesn't make sense.
As far as Kohl's, not a Capital One card has no bearing on if Kohl's will issue you a card they're separate. I got a Capital One card and a Kohl's Charge 2 weeks apart last year.
You said, "had been settled long ago", meaning the account went into collections and you paid it off?
If so or if the card was closed by them for poor account management then that's your reasoning. A lot of creditors hold grudges I've seen people with a bad account from the 90's try to reapply with scores in the high 700's be denied because of this issue.