Here are 2 other options.

WITH Contacts AS(

SELECT INS.INSPNO, CNT.FIRSTNAME, CNT.LASTNAME, CNT.CAPACITY,

ROW_NUMBER() OVER( PARTITION BY INS.INSPNO ORDER BY CASE WHEN Capacity = 'Contractor' THEN -1 ELSE INS.INSPNO END DESC) rn

FROM @inspection INS

INNER JOIN @INSPECTIONCONTACT CNT

ON INS.INSPNO = CNT.INSPNO

)

SELECT INSPNO, FIRSTNAME, LASTNAME

FROM Contacts

WHERE CAPACITY <> 'Contractor'

OR rn = 1;

SELECT INS.INSPNO, CNT.FIRSTNAME, CNT.LASTNAME

FROM @inspection INS

INNER JOIN @INSPECTIONCONTACT CNT

ON INS.INSPNO = CNT.INSPNO

WHERE CNT.CAPACITY <> 'Contractor'

UNION ALL

SELECT INS.INSPNO, CNT.FIRSTNAME, CNT.LASTNAME

FROM @inspection INS

INNER JOIN @INSPECTIONCONTACT CNT

ON INS.INSPNO = CNT.INSPNO

WHERE INS.INSPNO IN ( SELECT C.INSPNO FROM @INSPECTIONCONTACT C

GROUP BY C.INSPNO

HAVING MAX(C.CAPACITY) = 'Contractor'

AND MIN(C.CAPACITY) = 'Contractor')