The gun is not a shield, it doesn't prevent you from getting shot. It can only help you if you shoot first at any sign of home invasion. Most of the time it's just a family member or intimate acquaintance: http://www.nejm.org/doi/pdf/10.1056/NEJM199310073291506

The study sounds correct for what it studies. People who keep a gun in their home are more likely to accidentally kill someone else that they already know. That makes sense, since people without one aren't likely to grab a knife and run at a perceived threat. Even if they did, it gives more time for the other person to react and announce that they are a friend.

However, as an anecdote, most people I know of who actually know what they are doing (as in people who are gun enthusiasts, not people who bought a gun "for protection" and shot it enough to take a class then put it in a drawer) announce themselves before shooting as the goal is to get the intruder to leave.

Quite often this alerts the intruder to your location and, in the case that they are an actual threat, they will charge at you (this is counter intuitive for me, but most stories I've read of home invasion with an armed resident seem to end this way). I only typically hear about these stories from survivors, but the cases I know of the resident killed or wounded their attackers and were safe.

Basically, that long-winded group of anecdotes is to say that it is not the case that a gun can only help you if you shoot first at any sign of home invasion. Anyone who actually knows something about guns knows that you only point a gun at a target you have identified and are prepared to destroy. For the most part, that means you won't shoot first at any sign of home invasion.