Imagine that Chicago had held the 2016 Summer Olympics, which we tried strongly but ineffectively to win during the bidding process several years ago.

Then imagine four male Russian or Chinese or — how about this? — Iranian athletes saying on TV that they had been robbed at gunpoint by an armed man or men who posed as Chicago police, stopping the taxi the athletes were in, with one robber putting a gun barrel to the most famous athlete’s head and ordering all of the foreigners to lie on the ground and surrender their valuables.

How disgusted with our city would you be?

How strongly would you be thinking, “Can we do anything right?”

Then imagine that you found out, as the tale unraveled, that the four athletes were a lying bunch of partiers who basically made up the tale to cover up their own misdeeds.

You’d be more than a little outraged. You’d be furious that arrogant, drunken visitors had spread a falsehood that played into our own fears of inadequacy and impotence in the face of our seemingly endless and uncontrollable hometown violence. You’d be livid that we had been embarrassed in front of the world for something — at last — we didn’t do.

And finally, you’d be thinking the worst things about those already non-friends of ours — the Russians or Chinese or nuclear-wannabe Iranians.

Now you know how Brazilians feel about U.S. gold-medal swimmers Ryan Lochte, Jimmy Feigen, Jack Conger and Gunnar Bentz. And by extension, the United States.

Those swimmers could make a relay team of dumb-and-dumber ambassadors to any country. But they made a puddle of stink in a country that has been ridiculed so much for its Olympic unpreparedness, societal discord, political corruption and economic dysfunction that piling on with lies is a low-blow sin.

Especially coming from the U.S.A. Not everybody loves us, you know. Winning more medals, more championships, more Oscars, more Nobel prizes, more rap video awards than anybody else year after year doesn’t necessarily endear us to smaller, less rich, less vapid countries. They may envy us. They may be happy, in theory, that our free country exists.

But nobody likes an overdog unconditionally. And when that overdog arrogantly raises its hind leg on somebody’s couch, that’s a problem.

When Lochte told a U.S. television host in Rio that he and his pals had been robbed on their way home from a late-night party, it made world news. It played into what global critics had said all along: Brazil is an unsafe, backward-drifting, overgrown banana republic where your life is about as safe as a brook trout’s in the bay sewage.

Why Lochte said anything at all, without letting the police report play out, speaks to his idiocy and insulation and God knows what. Maybe he was still hammered.

When the purported gunman told the swimmers to lie down, Lochte stated on NBC’s “Today Show,” “I refused. I was like, we didn’t do anything wrong, so — I’m not getting down on the ground. And then the guy pulled out his gun, he cocked it, put it to my forehead and he said, ‘Get down.’ And I put my hands up — I was like, ‘Whatever.’ ”

Dude!

Red flag. Not even Spicoli from “Fast Times at Ridgemont High” would do the stoner thing with a cocked pistol barrel between his eyes.

Fact was, the four had knocked down a bathroom door at the gas station, urinated on a wall, acted like spoiled frat boys. They clearly forgot about things like surveillance cameras.

Lochte’s father, Steven, defended his son early on.

“Why would anybody fabricate anything?” he told the AP when the story was first questioned. “It’s just ridiculous.”

Well, Pops, talk to that kid of yours. You raised him.

Fines have been paid, new statements made, and all four swimmers are now safely on American soil. Lochte, who’s 32 with a seventh-grade maturity, said in a clearly lawyered-up statement on Twitter that he was sorry for his “behavior last weekend — for not being more candid and careful” in his description of that early-morning scene.

That’s pure America, too: the not-quite-repentant mea culpa.

Back in 1958, a best-selling political novel called The Ugly American was published. It described how wealthy, snobbish, unconcerned Americans were destroying Southeast Asia and the reputation of the U.S. by, well, being pigs. It helped create the Kennedy-era Peace Corps as a kind of penance.

This swimming episode in Brazil could almost be a new chapter to that book.

Or, whatever.

Follow me on Twitter @RickTelander.

Email: rtelander@suntimes.com