First of all, the Delta background check is true, a pilot for CAPPS II (see in the news forum for more info).
Secondly, the credit check is different from the credit check that happens when you apply for credit.
When Delta runs the credit check, it's akin to a marketing company running a credit survey to determine who to offer pre-approved credit cards to. This is usually noted in a different manner from the normal credit application check, and has no negative effect on credit whatsoever. In fact, a lender most likely won't even see these types of credit checks.
With that said, I dislike the process and think it's an invasion of privacy.