When you do the proper comparison, you find that easy access to guns lowers the mortality rate.
No such evidence exists since you can't prove a negative. This is why pro-gun people assume guns are a crime deterrent and try to back up the claims with faulty statistics like taking pieces of the Harvard paper you linked out of context despite there being a section of the paper that alludes to the following:
Let me introduce a single statistic - intentional homicide. The rate of intentional homicide is greater in the US (4.7) than Greece (1.7), Norway (2.2), India (3.5), United Kingdom (1.0), Australia (1.1), France (1.0), Israel (1.8), and Canada (1.6). I purposely chose these specific countries because they are either similar in cultural makeup or have just as much social-economic pressures that were mention in your single paper. If guns were an effective deterrent to crime and in particular homicide then the US, which values the right to bear arms second only to freedom of speech and religion and has the largest percentage of gun ownership for self defense (as mentioned by the Harvard paper), should be lower than the other similar countries.
Also I find it interesting that some states (Florida in particular) are banning doctors from asking about gun ownership even in cases of spousal abuse. If data would prove the pro-gun lobby's argument then why do they legislate barriers for collecting the data?