Tucker Carlson burst through the doors of Charlie Palmer Steak, enfolded in an entourage of producers and assistants, cellphone pressed to his ear. On the other end was Lachlan Murdoch, chairman of the Fox empire and his de facto boss.

Most of Fox’s Washington bureau, along with the cable network’s top executives, had gathered at the power-class steakhouse, a few blocks from the office, for their annual holiday party. Days earlier, Mr. Carlson had set off an uproar, claiming on air that mass immigration made America “poor and dirtier.”

Blue-chip advertisers were fleeing. Within Fox, Mr. Carlson was widely viewed to have finally crossed some kind of line. Many wondered what price he might pay.

The answer became clear that night in December 2018: absolutely none.

When “Tucker Carlson Tonight” aired, Mr. Carlson doubled down, playing video of his earlier comments and citing a report from an Arizona government agency that said each illegal border crossing left up to eight pounds of litter in the desert.