It looks like you want to call the 3 argument version of parse that doesn't take a reviver, but it is private (I'm not sure why.)
To call the 4 argument version, it looks like you will need to pass a Callable reviver instead of null.
What if you add your JSON string to the scope, and do this?
cx.evaluateString(scope, "JSON.parse(jsonString);", "parse.js", 1, null);