They qualify the above statement in the prior paragraph: "One reason why so many American police shoot first is that so many American civilians are armed."
http://www.pewresearch.org/fact-tank/2013/06/04/a-minority-o...
Arresting somebody who owns one or two guns is really not inherently safer than arresting somebody who owns a few crates of guns, so the number of guns in the country is irrelevant. The number of gun owners is relevant.
The apparent upward trend in police militarization and the number of Americans that own guns simply do not correlate. The Economist's unfamiliarity with American culture (particularly American gun culture) explains how they could make this mistake.
Police in America are less likely today to encounter guns than they were 40 years ago, but police shootings are apparently at all time highs. If their theory held water, that would not be the case.
Your hypothesis does not fit the data.
The thing is both sides are kind of wrong. London has far more gun crime than much of the US does (personally I ran into three firearms incidents without trying) which really should provoke much more soul searching in the UK than it does (they delude themselves into thinking the whole US is uniformly dangerous), however, British cops, while by no means perfect, are enormously less likely to be in aggressive by default mode. Obviously it does happen quite a bit, but nothing like the same antagonism that you have in North America.
Can we get a figure to back that up please? The MET places gun crime figures in greater London at 1570 (http://www.met.police.uk/crimefigures/) with a population of approx 8 million. Which American populations would you compare this to and what are their figures?
I've spent a significant amount of time in London and have never once run into any firearms incidents. It would be interesting to me to see the data behind this.
Whether or not this is a fair comparison is another matter.
Clearly, arresting a suspected drug dealer is far more dangerous in the US than in the UK - and widespread gun ownership is a reasonable explanation for that diference.