I'd just have them come out. Tell them you have X amount of active lines, and you are only seeing a problem on that receiver. With an HD DVR, it could be a number of things- dish alignment, corroded/improper fittings, or a multiswitch if applicable.
As an HSP tech, I know I don't inspect the system as deeply as I should as a service tech, as in if you report your problem on one receiver, I will start there. I will ask if your other receivers have been having a problem as well, or ask to see another receiver to find a like symptom. I'll still check and service the system from dish to IRD to find the resolution. But I won't inquire about missing receivers unless the receiver I am servicing isn't posted on the account and is giving me an error code other than 711 (service not activated). If they happen to ask, your receiver is in your RV, and if they want to see it, your brother has it in another state right now for a family vacation.
But you should be fine. I wouldn't worry about it unless something fraudulent is going on.