No point missed at all. The figures quoted are wrong. Directly from This article.

Gun violence in the United States results in tens of thousands of deaths and injuries annually.[1] In 2013, there were 73,505 nonfatal firearm injuries (23.2 injuries per 100,000 U.S. citizens),[2][3] and 33,636 deaths due to "injury by firearms" (10.6 deaths per 100,000 U.S. citizens).[4] These deaths consisted of 11,208 homicides,[5] 21,175 suicides,[4] 505 deaths due to accidental or negligent discharge of a firearm, and 281 deaths due to firearms use with "undetermined intent".[4] Of the 2,596,993 total deaths in the US in 2013, 1.3% were related to firearms.[1][6] The ownership and control of guns are among the most widely debated issues in the country.

So, the quoted figure of 5100 is well under the number of murders and massively under the total number of deaths. 11,000 by homicide alone. Almost another thousand due to accidents and undetermined causes. So your less than 0.000017 murders per gun is a massive under representation and if we put in the true figures - IE 12000 deaths / number of guns you have double that of the UK. I would also cast doubts on the number of guns given in both cases as well. The number of illegal, non-registered guns have not been been taken into account.

This does not account for the number of injuries either. I would postulate that the number of injuries due to firearms is going to be massively higher by proportion in the US than the UK.

As Stu has already explained, there are just too many guns and they are all to often in the hands of people that should not have them.

Scary fact for you here.

For every 100 people in the UK there are less than 7 guns. In the USA that is 112 guns per 100 people.

DtG