The damage insurance policy that you speak of will not cover theft of a DirectTV box. Those policies are specifically for accidental damage only. They do not cover theft or any damage resulting from a direct violation of your house rules or contract (i.e. - pet damage in a non pet friendly home).
If you cannot find out what happened to the box, then most likely you will have to replace it at your cost. Seems strange to me though that guests staying in your home would not let you know that the TV wasn't working. Even stranger is what someone would do with a DirectTV box? Weird.
This may not be possible, but could you try calling Direct TV customer service to see if they have any way of tracking exactly when the box was used last in your home? For example, if it is a DVR box, it might have been used to record a show and they may have a record of it. If Direct TV can do it, you will be able to pinpoint which guest was in the house at the time.
It's also possible they can locate the box if it's been reconnected to their network somewhere else using the unique ID assigned to all such network devices.
I don't know about Direct TV, but we have DISH in one place and Comcast in another, and all receivers have a stamped code that must be used to activate service on them. to a specific acct. # & address---- And is controlled by a central station
Long gone are the days when one could steal service from your neighbor by rigging outside cables to divert service, IF the customer has a service that requires a box..
You should check to see if you purchased a Service Agreement. If so, It may cover loss, etc.
I agree that it would be impossible to charge a guest without documentation that something " went missing" on a certain date.
Best of luck! Please let us know how this turns out!