Revert some string logic in valueHandler

Closes #3589832

This sort-of-reverts a logical change made in #3572908, which passed a value of FALSE along as an extracted field value, while previously we would have simply excluded this from the JSON. "Sort-of" because it does not go back to if ($value) but rather gives three explicit conditions.

We will need to revisit this as we add support for boolean fields, which we still want to do. Basically, that conditional needs to be smarter and check the schema to understand what "empty" values look like.