South Africa, banned from the Olympics after the 1960 Games because of its apartheid policy, could not have wished for a more affecting image of its return to the international fold: a white and a black African united in sport.
Over the following months, Meyer received hundreds of letters of congratulation from compatriots of all colours. What registered so clearly on that evening of high emotion in Barcelona's Montjuic stadium was the genuineness of the gesture. Meyer recalls the occasion almost reverentially. "Usually when someone finishes second they are really disappointed, but I was so happy because it had been such a long road just to get to the Games. I got a medal - lots of great South African athletes never even got the chance to compete in the Olympics. Even if I win a gold medal in the future it will never be as emotionally rewarding for me as getting that medal in Barcelona."
But such reflections have not taken the competitive edge away from the athlete who followed, and eventually surpassed, her South African contemporary, Zola Budd. Meyer is determined to achieve the success in marathon running that she experienced on the track, where she added a Commonwealth silver to the one she won in Barcelona, as well as a World Cup title.
Budd - whose adoption by the Daily Mail and then Britain in the mid-1980s allowed her the international competition denied to her compatriots until 1992 - has retired from top-class running. Meyer is still there. And, by her own assessment, training and running better than ever before.
She is not big - five foot three inches and not quite eight stone - but her ambition remains huge. This, after all, is an athlete who is unable to run anymore. At least, according to the assessment of doctors who examined her in the wake of the severe Achilles tendon injury which forced her to abandon the 1996 Olympic marathon.
She suffered a 70 per cent tear of the tendon, and the prognosis was bleak, indeed terminal. But the doctors reckoned without the spirit that had kept Meyer running and improving through the long years of international exile. "I didn't believe what they said," she recalled. "Something deep down inside me said I would be back. I believe there is nothing you can't recover from."
It is just as well that Meyer holds such a philosophy. Over the past five years it has been tested to the limits by a succession of injuries to her legs and back. She even managed to cause a stress fracture in her spine while lifting heavy luggage from an airport carrousel on her return from the 1995 World Championships in Gothenburg.
Since July of last year, however, she has enjoyed uninterrupted training for the first time since 1994, when she set her marathon best of 2hrs 25min 15sec on her debut in Boston. And a winning time of 66min 44sec in January's Tokyo half-marathon - the second fastest ever by a woman - confirmed that, at the age of 32, she is in the form of her life.
"Until now I have approached marathon running with the mindset of a track runner, and that doesn't work," she said. "Now I feel like a marathon runner, and that transition makes me excited about running in London."
Her recent advances have taken place in tandem with the coach who has overseen her running for the past 14 years, Pieter Labuschagne, who also guided Budd's fortunes. "Elana can go much faster than ever before on Sunday," he says.
If Meyer does succeed in her London ambition, she will not be the first woman to have won there after being told her career was finished. Liz McColgan, who took the title in 1996, received the same prognosis two years beforehand.
If Budd was Meyer's main rival in the early part of her career, it was McColgan who took over the role. Although South Africa only returned to international sport in 1992, Meyer had competed against the Scot many times before both lined up for the Olympic 10,000m final. That is, she had competed theoretically.
"By 1991 I was getting so frustrated with not being able to race against runners from other countries that I competed with Liz on paper," Meyer said. "Every time she ran well, at 3,000m or 5,000m, I would go out back home and try to run faster."
She succeeded, too, recording 8min 32sec for the 3,000m and 14min 44sec for the 5,000m, times which still put her in the world's top five.
She even went out to Tokyo with her husband Michael - a trained lawyer who now runs a chain of children's sportswear shops near their home in Stellenbosch - and witnessed McColgan winning the world 10,000m title.
"It was not nice," said Meyer with a wry grin. "I hated every moment of it, because I so wanted to be running myself. I won't say I would have won - but I know I would have made a real race of it."
This time around, it is Meyer who has the opportunity to take the limelight at McColgan's expense - the Scottish runner misses this year's race because she is expecting her second baby.
Seven years ago, Budd said Meyer would one day run 2.20 for the marathon. Reminded of that forecast this week, Meyer readily agreed with it. "Yes, for sure," she said.
"On the track, and in half-marathons, I've achieved close to my potential. In the marathon, I haven't. That's something which really motivates me."
How much, we may see tomorrow.