Hillary Clinton became “overheated” and left a Sept. 11 memorial service abruptly after an hour and a half. Television cameras were rolling, allowing much of the world to see her being loaded into her van. She went to her daughter’s nearby apartment for a breather, emerged looking chipper, stopped for a picture with a child and drove off.

If it had ended there, the incident would have been unfortunate, but wouldn’t have altered the course of the campaign. Instead, the public learned later that Clinton had been diagnosed with pneumonia on Sept. 9 and neglected to tell anyone.

The lack of transparency played right into Donald Trump’s hands. Clinton began her career as a staffer on the Watergate hearings, yet she has repeatedly ignored the central lesson of the scandal: It’s not the crime that gets you but the cover-up. Pneumonia is hardly a crime and neither is a private server, but by covering up both she made them seem worse. On Labor Day, she brushed off a coughing episode in Ohio merely as evidence that she is “allergic to Trump.” But four days later, a doctor put her on antibiotics for pneumonia and she didn’t find it worthy of comment. Too bad she didn’t get a prescription for truth serum.

Now the burden is on her to prove she’s fine. She would have to drop and do 20 push-ups to satisfy Trump that she is. Just as he tried to delegitimize Barack Obama with birtherism, Trump has tried to Swift Boat Hillary by delegitimizing her physically. For months, the Republican nominee has been stoking the charge that something serious is wrong with her physical and mental “strength and stamina.” His wingman, Rudy Giuliani, directs voters to go to the Internet and look up “Clinton illness” and watch a ginned-up video that makes it look as if Clinton is having a seizure. After the coughing, Trump tweeted that the media wasn’t covering it enough.

Henceforth it will all be covered — every sniffle and every pause that could be a sign that her mind is going. In addition to his medical diagnosis, Trump has taken to charging that she doesn’t “look presidential,” a catch-all that adds the dig that the little lady keeps a light schedule so that she can get home to bed early and isn’t, obviously, a perfect male specimen of health like Trump himself, even though, at 70, he’s two years older.

Trump himself has been somewhat wanting when it comes to his health records. First, he made public a laughable letter from his doctor — idiosyncratically addressed “To Whom My Concern” — that echoed Trumpian grandiosity with the assessment that the Donald would be “the healthiest individual ever elected to the presidency.” Then, with a good sense of timing, Trump got a physical last week, presumably at the hands of another physician, which he is releasing any day. He’s set to appear Sept. 15 on “The Dr. Oz Show” to unveil “his personal health regime,” presumably without pictures of his fast-food habits on his plane.

After the episode Sunday, he knew enough to let the facts stand for themselves, congratulating himself for taking no “satisfaction” in her troubles. On Fox News on Monday morning, he sent her a Hallmark card hoping “she gets well soon.” He inched back to his usual self a bit later on CNBC, saying, “It was interesting because they say pneumonia on Friday but she was coughing very, very badly a week ago and even before that this wasn’t the first time.”

Getting pneumonia doesn’t mean you’re unhealthy. It’s one of the many occupational hazards of the endurance trial a modern campaign is. But she’s going to have a hard time proving she’s healthy now.

Imagine an alternate drama. Clinton reveals before the weekend that she has pneumonia. She soldiers on. She kept her schedule, including the LGBT fundraiser with Barbra Streisand where the candidate offered her controversial description of some Trump voters as “deplorables.” She was up early Sunday, but the crowd, the sun (New York Congressman Joe Crowley said that he and Sen. Chuck Schumer had soaked through their suits), and the sadness of the day were too much and she left after an hour and a half. Most people would think she was a trouper to play through the pain and wish her a long nap in a cool room with a bowl of chicken soup.

Instead, much of Sunday, no one knew what was going on. Information dribbled out. Her motorcade back to her home in Chappaqua, N.Y., was covered like O.J.’s ride in the Ford Bronco. Hours later, a statement from her doctor came out. That’s no way to overcome a trust deficit.

Still, Clinton has nine lives. Terrible things happen — having to stand by her man after Gennifer Flowers, Whitewater, the health care debacle, Monica. But she has repeatedly turned adversity into triumph, not least by becoming the first first lady to leave the White House a year early and win a Senate seat in a state she’d only visited as a tourist. She’s now the first female candidate for president. Memo to Trump and the men who love him: Underestimate her “strength and stamina” at your peril.

Margaret Carlson is a Bloomberg View columnist.