(SELECT s.score as myscore,s.teamID_FK as me,s.opp_teamID_FK as them from score s where s.teamID_FK=23)
UNION
(SELECT t.score as theirscore,t.opp_teamID_FK as me,t.teamID_FK as them from score t where t.opp_teamID_FK=23)

yields:

 myscore   	  me   	  them
1770 	23 	25
1210 	23 	30
2080 	23 	29
1970 	23 	25
1650 	23 	30
900 	23 	29

theirscore doesn't even appear!