DURHAM, N.C.—On Sunday, a cable-TV documentary is scheduled to shower glory on Christian Laettner and Brian Davis for the back-to-back basketball national titles they helped deliver 20 years ago to Duke University.

But later next week they have a court appearance in Washington, D.C. It's about a loan their real-estate company failed to repay to former Duke captain Johnny Dawkins. The judge in the case, having last year ordered Laettner, Davis and a company of theirs to pay Dawkins $671,309, will decide whether to hold them...