Update Statement using Join and Group By

You can try putting the group by inside of a subquery, then join by the "JobOrderID", like this:

UPDATE J
SET J.StatusID = A.statusId
FROM MKT_JobOrder J
INNER JOIN (
    SELECT J.JobOrderID
        , CASE 
            WHEN SUM(DUV.VendorDUQuantity) = SUM(RD.InvoiceQuantity)
                THEN 1
            ELSE J.StatusID
            END AS statusId 
    FROM PLN_DU_Vendor DUV
    INNER JOIN ENG_Release R ON R.ReleaseID = DUV.ReleaseID
    INNER JOIN ENG_DU_Header H ON H.ReleaseID = R.ReleaseID
                               AND DUV.DUID = H.DUID
    INNER JOIN MKT_JobOrder J ON J.JobOrderID = R.JobOrderID
    INNER JOIN MKT_CustomerOrder CO ON CO.OrderID = J.OrderID
    LEFT JOIN PMT_RFDHeader RH ON RH.JobOrderID = J.JobOrderID
    LEFT JOIN PMT_RFDDetail RD ON RD.RFDID = RH.RFDID
                               AND RD.DUID = DUV.DUID
    WHERE CO.OrderID = 100
    GROUP BY J.JobOrderID
           , J.StatusID
    ) A ON J.JobOrderID = A.JobOrderID

User sub query instead to perform this operation

UPDATE 
   J
 SET StatusID = x.Status
   FROM 
   (select CASE WHEN SUM(DUV.VendorDUQuantity) = SUM(RD.InvoiceQuantity) THEN 1 
    ELSE   J.StatusID END as Status 
     JobOrderID
     FROM
    PLN_DU_Vendor DUV
    INNER JOIN ENG_Release R ON R.ReleaseID = DUV.ReleaseID
    INNER JOIN ENG_DU_Header H ON H.ReleaseID = R.ReleaseID AND DUV.DUID = H.DUID
INNER JOIN MKT_JobOrder J ON J.JobOrderID = R.JobOrderID
INNER JOIN MKT_CustomerOrder CO ON CO.OrderID = J.OrderID
LEFT JOIN PMT_RFDHeader RH ON RH.JobOrderID = J.JobOrderID
LEFT JOIN PMT_RFDDetail RD ON RD.RFDID = RH.RFDID AND RD.DUID = DUV.DUID                 
WHERE 
    CO.OrderID = 100
 GROUP BY 
    J.JobOrderID) X
 INNER JOIN MKT_JobOrder J On x.JobOrderID = J.JobOrderID