The bodies of the San Bernardino victims were still warm, and President Obama conceded that officials didn’t “know that much yet” about the circumstances or motives of the killers. But that didn’t stop him from exploiting the moment to call for more gun control. There was the usual shopworn pitch for “stronger background checks.” There was also a demand that anyone on the “no-fly” list be prohibited from buying guns.

“We have a no-fly list where people can’t get on planes,” Obama told CBS News, “but those same people who we don’t allow to fly could go into a store right now in the United States and buy a firearm. … That’s a law that needs to be changed.”

He repeated what has become a standard Democratic talking point in his Oval Office address Sunday evening. “Congress should act to make sure no one on a no-fly list is able to buy a gun,” Obama insisted. “This is a matter of national security.”

But if people on the no-fly list and the even more comprehensive terrorist-screening watchlist pose such an urgent threat to national security, why haven’t they been arrested? If horrors like the San Bernardino massacre could have been prevented by incapacitating the individuals on the watchlists, surely it is sheer recklessness to do nothing until they try to board a plane or buy a gun.

Well, maybe — except that the San Bernardino butchers weren’t on any government watchlist. Neither was the Colorado Springs gunman. Or the mass shooter at the Oregon community college. There are an estimated 47,000 people on the federal no-fly list — but Dylann Roof, the Charleston church killer, was never among them. Nor were Boston’s Tsarnaev brothers. Nor was Adam Lanza, who murdered 26 victims at the Sandy Hook Elementary School. As far as is known, no perpetrator of any mass shooting in the United States has turned out to be on the no-fly list.

On the other hand, the late Ted Kennedy was on the list. At least five times in 2004, the senior senator from Massachusetts was denied a boarding pass because the alias “T. Kennedy” appeared on the no-fly list. Each time it took the intervention of Homeland Security officials to clear him for travel — and it still took Kennedy and his staff more than three weeks to get his name removed from the list.

Others blocked by the no-fly list have ranged from Washington journalist Stephen Hayes to a Florida toddler to Congressman John Lewis of Georgia to singer Cat Stevens. Even agents of the Federal Air Marshal Service have been swept up in the no-fly net. There is nothing transparent about the government’s formula for adding names to the no-fly list, and there is no due process for getting one’s name cleared. Until recently, the government wouldn’t even confirm that someone was actually on the list. Only after the ACLU prevailed in a federal lawsuit last June did that finally change.

Even more opaque and unreliable than the no-fly list is the gargantuan Terrorist Screening Database. The government has conceded in the past that it “misidentified” tens of thousands of blameless individuals, yet it continues to add names at a staggering rate. In court filings in 2014, federal officials disclosed that more than 1.5 million names had been added to the terror watchlist in the previous five years. Data from the National Counterterrorism Center indicate that of 680,000 names on the terror watchlist in 2013, more than 40 percent were described as having “no recognized terrorist group affiliation.”

With a little bad luck, anyone could find himself added to these terror watch lists run amok. To propose making rosters so sloppy the basis of draconian new limitations on a core constitutional right isn’t “common sense” gun control, merely cynical grandstanding.

Jeff Jacoby is a columnist for The Boston Globe.