More than 20 years on, Evans was in another, far happier Olympic context - present with a small group from Los Angeles 2028 for the International Olympic Committee (IOC) Coordination Committee’s first visit to their former bid rivals Paris, who are preparing to stage the 2024 Games.

Full of energy and looking pretty much the same as she did when she was winning Olympic and world swimming titles for the United States in the late Eighties and early Nineties, Evans embodied what just might be a model for future Games, in which partnership, rather than rivalry, is paramount.

The IOC’s historic decision to make a double Olympic award at its session in Lima last September - like FIFA, only sensible - was accompanied by a mantra – “win-win-win”.  Everybody wins – Paris, LA, the IOC. Nobody loses. And all cooperate. It was like a new kind of Olympic Truce. And the LA presence in Paris this week exemplified it. 

"It was beautiful here," said Evans, glancing around her at the view from the glass-walled meeting room at the top of the Hotel Pullman Paris Tour Eiffel, the city laid out in late afternoon sunshine, the rounded domes of Sacre Coeur pale on their distant hill, the midsection of the eponymous tower looming huge to her left.

"I enjoyed collaborating with Paris instead of worrying about what we were both doing. It was great to be amongst friends now. I loved the venue tour yesterday - I think the Stade de France next to the Olympic Village next to the swimming is fantastic.  I wouldn’t say it was a surprise, but it was really fun to see. It was super-exciting. I feel we are on a very good track.

"It’s been an honour to be here, to learn and listen and to integrate with the IOC, to see how we can have a 2024 Games that are incredible, and to piggy-back on that for 2028.

"These last few days have marked a great start to the partnership, which we hope will last for six more years and longer."

Fittingly, Evans - who was vice-chair and director of athlete relations of the Los Angeles bid - was sitting alongside Paris 2024, in the form of chief executive Etienne Thobois, and the IOC, represented by its Executive Director for the Olympic Games Christophe Dubi.

These two articulated their views of how this New Warm might work out.

"The IOC ideal in making the double attribution was that we had something to gain, which was - how do we re-think the delivery model of the Games?" said Thobois. "That is what we are very committed to doing.

"There is expertise and knowledge on both sides which means we can benefit from each other.

"Paris starts first, but there are areas in the two hours of discussion we had on Sunday and worked out very concretely the areas where we can best collaborate.

"These are things that are of the utmost importance when you talk about delivering the Games - the Village, how do you manage the venues, the digital strategy.

"These are areas where we believe we should work together with the IOC and Los Angeles 2028. And in some cases, we can create more concrete programmes and working groups in which one or the other can take the lead.

Dubi added: "The whole thing has to be practical. We will have a workshop in LA at the end of August. And there we are goIng to speak innovation - let’s project ourselves in the future, Paris and LA, and look at what could be the innovations in areas such as transportation, venue management, event delivery.

"We will also discuss about 'turn-key' solutions. In Agenda 2020 the IOC wants to acquire long-term solutions so that the organising committees do not have to re-invent them.

"If Paris and LA can collaborate and source one solution for the two Games, that’s a big gain."

Asked if a new model of collaboration had been part of the IOC calculations as they sought not to disappoint one of two hugely credible bids, Dubi responded "When we spoke in Lima about the triple win, there was a tri-partite agreement in which areas of collaborations were outlined. It was about collaboration between the two cities, whose Mayors know each other very well.

"There were promotional activities, and there were also ideas around staff training and staff exchange.

"So yes, that was definitely the vision at the time, it was sitting at the heart of the ‘triple win’."

Thobois took up the theme. "For instance the IOC is helping us in our programme delivering the scoring and timing. This is a real turn-key solution. There might be other areas like ticketing. This needs to go to tender, and then marketing. Things evolve. But at the end of the day the backbone for the system stays the same.

"And there are other areas that are more about methodology and how we can actually have the experience of the IOC and others – it’s an open book.

"We will do things on the legacy front, and on the education front. We will do things that we will be able to share.

"As Christophe says to us, it about having a direct line of communication which allows us to piggy-back stuff."

“Yes,” Evans responded. "That’s what’s important - a direct line of communication.

"Collaborating with the IOC, and collaborating with Paris 2024 - we don’t Know exactly what is going to come out of it, but it’s a very exciting prospect. We have years to pick each others’ brains and to understand these incredible things we can do together."

It certainly sounds good.