At the theatre on Saturday night, I watched Diana Nyad, the long-distance swimmer, ignite an audience for over an hour. She recounted her record-breaking 111-mile swim from Cuba to Florida at the age of 64 after several failed attempts, and in the face of killer sharks, deadly jellyfish and huge waves. It was like listening to a one-woman version of the Iliad, an almost too perfect literalisation of inspirational metaphor. The subtitle of the show was “never, ever give up”, a well-worn sentiment that in Nyad’s hands was made thrillingly new.

As it happens, the Clintons were in the audience at New York’s Minetta Lane Theatre that night. Afterwards on the pavement with one eye on the SUV convoy, theatregoers joked that Nyad’s words risked inspiring Hillary – God forbid – to have another crack at the White House. A few days later, Hillary and Chelsea appeared on the TV show Good Morning America to promote their book, The Book of Gutsy Women. To the question, “What’s the gutsiest thing you’ve ever done?” Hillary replied, “Ah, boy, I think the gutsiest thing I’ve ever done – well, personally, make the decision to stay in my marriage.” The bravest thing she’d done in public was run for president, she said, and in both scenarios the trick was to “just get up every day and keep going”.

Staying in one’s marriage is different to running for president, which is different to swimming 111 miles across the Gulf Stream – and I’m not convinced that “keep going” is the mantra for all of them. The mapping of motivational sports psychology on to every tricky situation in life – Get Brexit Done springs to mind – is a standard approach that in complex times seems increasingly unhelpful. It’s good to puff oneself up and feel infused with power and purpose, but when being motivated is the aim, rather than the byproduct of an undertaking, it seems like a misguided application of that energy.

If it’s a reflex branding issue, the oddest context to which it’s applied is the personal. Perhaps for Hillary, staying in her marriage was the right thing to do. But spinning it as courageous relative to the cowardice of leaving seems like a pinched and self-punishing way to audit one’s emotions. Cowardice and bravery are terms that, surely, have no place in this arena, if for no other reason than the need to preserve a single space in life safe from the win-or-lose framing device of Nike-ad type language.

Perhaps I’m just being defeatist: there’s an extension of motivational psychology for that too. A whole body of literature exists giving us permission to launder our own shortcomings by reselling them back to us as strengths. It’s OK to fail; it takes greater courage to admit to being wrong than to plough on down an erroneous path. I agree with all of these things, and yet framing them this way – as stealth virtues – triggers tired thoughts about the integrity of just giving up.

In the show on Saturday night, Nyad spoke of being molested as a teenager by her swimming coach. It was moving, and infuriating, the absolute predictability that this should have happened; that on top of everything else, there was that. The swimmer didn’t spin it as anything other than fact. Not grist for a survival story, nor something she’d overcome to become a better person. It was simply a traumatic event, plainly stated, in which the telling itself was the endurance. Truly, it was inspiring.

• Emma Brockes is a Guardian columnist