Replace NOT operator with explicit `false` check - part 5 (#68360)

Part 5.

We have an in-house rule to compare explicitly against `false` instead
of using the logical not operator (`!`). However, this hasn't
historically been enforced, meaning that there are many violations in
the source at present.

We now have a Checkstyle rule that can detect these cases, but before we
can turn it on, we need to fix the existing violations. This is being
done over a series of PRs, since there are a lot to fix.