You could definitely do that, but you guessed right. There is no way to assign remote codes to one box and not the other. The DVR and Mate use identical remote controls.
I'm surprised that this type of device at this price point doesn't include multiple IR codesets. The issue is pretty easy to solve in any case, though not necessarily for free or cheaply.
Right off the bat, my first recommendation would be to use a remote that support RF communication with a base-station that has IR transmitters. SUch as one of URC's Complete Control line along with its MRF base. That way you can use stick-on emitters to each device and both will receive the same kinds of codes, while still addressing them individually via the remote setup.
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