The department of social services shall recognize the Part C early intervention system established under sections 160.900 to 160.925 as an eligible program and shall pay all claims for reimbursement for Medicaid-eligible children to the Part C early intervention system. For those eligible children having other private insurance, the department of social services shall seek reimbursement as appropriate from the lead agency for payments made to the Part C early intervention system for covered benefits provided by health benefit plans under section 376.1218.