I don't have time to go do any research, but a couple of things come to mind as I read this.
1). How many deaths are caused by smoking, fatty foods, alcohol, falls and our old favorite, car accidents? So should we outlaw those things?
2). So where would the person writing this article be on the "right to die"? I'd guess they would be very much in favor of it -- Dr assisted suicide and all that. I don't like to see society "making suicide easy", by saying "just go into your doctor and he will help you". Because down that path it isn't very far to "our best advice is to kill yourself". It just seems odd to me to see an anti-gun person saying that a constitutional right has to be given up "because some might kill themselves".
3). I suspect the "gun homes are more likely..." has a causality problem. Folks that have guns to protect their home and family are more "responsible". In cultures where people take responsibility, suicide rates are higher -- Japan, China, etc ... "face is lost" and they feel like "suicide is the only way out". I disagree with the choice, but making taking responsibility illegal isn't going to fix it, and most likely will make it worse. The Scandinavian countries have worked hard to remove personal responsiblity from life, and they are plagued with a very high suicide rate -- and I'd bet it isn't predominately from guns.