Automatically checking / un-checking inputs.

Here's what i'm trying to do:

I have a list of inputs, when you select a child input, all parent inputs need to be check marked. If you uncheck a parent input, all checked children need to be unchecked.

I found this example online - it replicates the desired functionality perfectly:
http://jsfiddle.net/3y3Pb/14/

However, even though my markup is structurally similar to the example (ul > li) it doesn't work with my markup. This markup is coming from a WordPress plugin that I can not modify.

You can see my code (with markup here): http://jsfiddle.net/3y3Pb/223/

I've narrowed it down to the

<label>

Select allOpen in new window

element that seems to be wrapping each input. If I remove the label the example code works fine.  Since i'm not able to remove the label, I need a solution that works with markup in the above example.

Here's a demo of the same code without the label working as intended: http://jsfiddle.net/3y3Pb/225/