• By MARY ANASTASIA O’GRADY

Aída Zaldumbide was recuperating from heart surgery at the police hospital in Quito Thursday when Ecuadoran President Rafael Correa arrived there, asking to see a doctor. He had been in an altercation with some members of the national police at their barracks across the street.

We’ll get to the details of that scuffle in a minute. But it’s what happened next that matters most. Mr. Correa says that, once inside the hospital, the police “kidnapped” him for 10 hours, in what he is calling an attempted coup d’état.

Not so, says Ms. Zaldumbide, at least one other patient, and two doctors and a nurse who were on duty at the time. They say Mr. Correa retained all his presidential privileges and was never without the protection of his security team.

They also say he was offered an armed escort to leave but refused it. Ecuador’s minister of internal and external security has also said that the president was never detained.

Nevertheless, at 9 p.m. Mr. Correa, who was doing telephone interviews with the state-controlled media during the time he was supposedly “kidnapped,” ordered 500 army troops to the hospital. The soldiers arrived with tanks and submachine guns and opened fire on the police. A fierce gun battle lasted 40 minutes, took the lives of two men, and terrified hospital staff and patients.

Officialdom jumped on the side of Mr. Correa. On Friday, State Department spokesman P.J. Crowley seemed to cheer the overwhelming use of force. The police uprising “to some extent, did represent a challenge to the government,” he said, concluding that “the government responded effectively.” Eyewitness accounts and verifiable facts say otherwise.

The trouble started on Thursday morning when the police announced a strike to protest cuts in their compensation. Mr. Correa responded by going to the barracks to confront the cops. Once inside the building he went to a window, tore open his shirt, and shouted, “If you want to kill the president, kill him!”

If the goal was taking out the president, that provocation provided the moment to do it. But it is unlikely that the police had any such thing in mind.

This is because, despite feeble management of the economy, most polls give the populist demagogue an approval rating of better than 50%. Recent history suggests that Ecuadoran governments topple only after their public approval falls first. Without popular support to remove Mr. Correa, a coup—by all accounts there was no leader—was not going to happen.

It is true that the “blue flu” and police roadblocks in Quito had spread to other cities, and that the police used tear gas and threw things at Mr. Correa when he went to the barracks. That’s when he walked across the street to the hospital, his notorious macho dignity obviously wounded.

After the shootout was over, Ms. Zaldumbide told the Ecuadoran daily Expreso this: “It is unjust what happened. The press here is talking about him being kidnapped but it wasn’t that way. The special forces made a cordon for him to be able to leave but he did not want to. We told him to leave, to put our lives first, but he did not want to.” Ms. Zaldumbide went on to say that Mr. Correa “insisted on having [his movement known as Alianza Pais] come to escort him out because he had to leave with his head held high.”

Dr. Fernando Vargas, who was working at the hospital, posted similar testimony online at ecuadorenvivo.com: Mr. Correa “was never kidnapped, was attended to by hospital personnel,” and “the minister of the interior was in permanent contact with him.” The police prepared an armed escort for him and waited two hours for him to make use of it. Instead, there was “a savage military assault on this hospital,” where, the doctor pointed out, there were women, children and old people.

Diego Chimborazo, a police officer who was in the hospital for knee surgery, and another doctor gave similar accounts to Expreso of the senseless military strike.

Mr. Correa had little trouble managing the story. In the morning he closed down independent television reporting, limiting Ecuadorans to his version of the day’s events. Curiously, when he arrived at the plaza in front of the presidential palace—shortly after he left the hospital—to celebrate his triumph over the “coup,” giant TV screens and a sound system were already in place.

There is some evidence that the military, which will also bear Mr. Correa’s austerity measures, sympathized with the police strike. It did not move to police city streets when lawlessness broke out, and the air force closed some airports. Yet throughout the day the top brass remained loyal to the president.

One thing is certain: Mr. Correa is not going to let the crisis go to waste. Since Thursday he has been seizing the airwaves to broadcast his version of the narrative, which implicates his political opponents in what increasingly looks like a coup that never happened.

Write to O’Grady@wsj.com