This wall-wart may be made with fuseable magnet wire (dictionary spelling would be fusible, but I see fuseable more often). In the state the supply is in right now, following the "output loading" test that was accidently performed, it should still pass a 3000 VAC hipot test from primary to secondary (2000 VAC for 120V equipment). If not, then someone messed up.
Are you sure there isn't a thermal fuse up against the primary winding under the first two layers of tape?