I don't want it downloaded/run simply due to company policy (our network admin's request). I would prefer pushing out updates as well, however certain circumstances prevent this from effectively working.

The computers that are an issue are the remote laptops outside the building. We typically push out the updates while the computers are connected to our network, but before being deployed we turn on Automatic Updates to make sure they get the latest updates. Not all computers on our network use Auto Update because we prefer to test the update (for compatibility issues more than anything else) before pushing it out.
The laptops are a unique situation. We prefer to have them as secure as possible, and therefore the Auto Update is turned on. This allows the laptop to update Windows even if they are not connected to our network via VPN or other means.

Other than that, I could not explain why the network admin prefers to NOT use this tool. But the policy is set NOT to use this tool, therefore I look for easy ways to avoid it. There doesn't seem to be any easy way to avoid it, other than going through the routine of cancelling the install.