{"approved": false} and {} get the same answer from allow if input.approved == true. The answer is undefined, not false.
The host takes an object with an optional boolean approved field and permits work only when the query returns true. The rule is complete and has no default. Neither input makes it succeed, so allow is undefined in both. An explicit false result would be a different outcome, and the host has to know which one it got.
Two ways out. Add default allow := false and both inputs return false. Or keep undefined and make the host handle it explicitly. Either way the host decides what an absent result means. I can argue for both and haven't picked one.
Neither option checks that the input document exists or that approved is actually a boolean. That is input validation, and it happens before the query.