Not true.
If a contract comes to the court and a judge finds in favor of the defendant and orders the loan to be paid, the judge is bound to allow installment plans. However, if there is non-compliance with the order from the court the party is guilty of civil contempt. Civil contempt can (and does) result in jail time. I have made the judgment ICly that contempt of court is appropriate in cases where the court issues a judgment and a party fails to pay.
You are confusing the ideas from the Bankruptcy Reform Act of 1978, William v. Illinois, Tate v. Short, and Bearden v. Georgia that relies on the idea that someone cannot get out of jail due to public or private debt. That's not really applicable here, nor would it ever be applicable as there are set prison/jail times for each charge on LSRP.