The current issue of The Economist contains a striking factoid: “Last year, in total, British police officers actually fired their weapons three times. The number of people fatally shot was zero.” By contrast, there are about 400 fatal shootings each year by local police in the United States.

When I tweeted out this stunning stat earlier this week, no shortage of people noted an obvious explanation for why British police were so much less likely to fire their guns: there were far fewer guns around them. The U.K. has some of the world’s strictest limitations on gun ownership—handguns are all but prohibited, while shotguns and rifles require a police certificate and special justification (self-defense does not qualify.) There are an estimated 14,000 handguns in civilian hands in the U.K. (population 63 million) and slightly more than 2 million shotguns and rifles. Estimates for the number of total firearms in civilian hands in the U.S. float north of 300 million. Simply put, if the police in the U.S. seem a lot more on edge than those across the pond, they have good reason to be.

As obvious as this explanation for the militarization and trigger-happiness of U.S. police may be, it has gotten relatively little attention amid the alarming spectacle that has played out in Ferguson, Missouri following the fatal police shooting of an unarmed black 18-year-old and, more recently, the fatal shooting just a few miles away of a mentally-ill man holding a knife. That oversight may be partly because this aspect of the debate undermines one of the most popular media narratives to emerge from Ferguson: the notion of a growing right-left coalition united against heavy-handed police tactics.

There is indeed agreement between many liberals and libertarians that the militarization of the police, especially in its dealings with racial minorities, has gone too far. But this consensus may crumble pretty quickly when it’s confronted with the obvious police counter-argument: that the authorities’ heavy firepower and armor is necessary in light of all the firepower they’re up against. At that point, many liberals will revert to arguing for sensible gun control regulations like broader background checks to keep guns out of the hands of violent felons and the mentally ill (the measure that police organizations successfully argued should be the gun control movement’s legislative priority following the Newtown, Connecticut shootings) or limits on assault weapons and oversized ammunition clips. And liberals will be reminded that the libertarians who agree with them in opposing police militarization are very much also opposed to the gun regulations that might help make the environment faced by police slightly less threatening.

The inherent tension in this nascent right-left alliance was laid out in sharp terms this week by Josh Horwitz, head of the Coalition to Stop Gun Violence. He noted that the ballyhooed caution against police militarization by Rand Paul, the libertarian senator from Kentucky, looked a bit more dubious in the broader context of Paul’s politics: