Jeff, I think others have already answered your question for you, but I'll add one additional item for you to consider.
A HUD investigator won't even need to visit your house to determine that you are not living there. As someone who worked on fraud cases for the US government while overseas, I can tell you that a simple Lexis Nexis search of your property's address will bring up anything and everything that has ever been recorded at that address.
What might that include? Well, your tenant's vehicle registration, their registered address for voting purposes, any requests to the post office to hold mail or forward to the address from their prior residence, etc. Any type of action with the government will be gathered in one easy place for the inspector to see. And it takes all of two seconds to type that information into a database and get some results. (I actually tried it on myself - scary what Info they can gather in one spot...down to the mortgage amount I owe on property!)
Given that you are on a real estate investment site like BP, I would imagine that this property is probably the tip of the iceberg, and you have the intention of purchasing more. Do you really want to jeopardize all that just to make one lousy deal without even putting out any effort?
My guess is, probably not. Do the work my friend, and the deals will follow.