This commit restores the logic in Handler that was changed when
d20ac56a was merged, while leaving the structural improvements intact.

In addition to a couple of changes where a typo meant the wrong
variable was being referenced, some logic branches now return false
rather than called super. This realigns our Handler's behaviour with
that of the JDK's.

Some more tests have also been added to try to catch the problems that
were introduced during the merge.

Closes gh-7021