Veldman and John Hunter were part of the eight at Mexico City in 1968 who, Veldman reckons, should have won the gold.
"We were hot favourites but the wheels fell off. We should have won it - finished fourth, got nothing, a terrible experience," Veldman said. He vowed then to press on, no expense spared, for 1972.
The eight had beaten the feared East Germans, state-sponsored and at the start of the era in which their sports programme was belatedly largely discredited over systematic doping, at the European championships in 1971. The same crew was retained for Munich.
"The critics said 'you'll never do it twice in a row'," Veldman recalled. "But they panicked, changed their crew and I think their 1971 crew was better than 1972."
There was nothing lucky about the win at Feldmoching. New Zealand were out in front early and simply too good.
Veldman, a forthright and gregarious character, won 21 national titles in a long and satisfying career. But he's adamant - Munich was the "absolute pinnacle".
"The boys would probably crucify me for saying this, but it was one of the easiest races in my career.
"It was so perfect, just a case of tapping it along."
The day gained extra lustre at the medal ceremony. To their surprise, they heard the strains, not of the expected God Save the Queen, but, for the first time, God Defend New Zealand.
"We were bawling like babies," Veldman laughed. He said the person responsible was a German liaison man. "It was totally unexpected. Awesome."
The black and white film unquestionably added to its place in sporting history.
Veldman praised their coach Rusty Robertson: "He was brilliant. I look at him, Arthur Lydiard, Lois Muir and the Needle, Fred Allen. All incredible people who were able to motivate those in their charge to do wonderful things."
It was the day, Veldman reckons, that "New Zealand rowing came of age". There had been earlier successes - notably a coxed four gold, four years earlier, but none with the resonance of this.
Before the regatta, Don Rowlands, one of the most significant figures in New Zealand rowing, had stickers made, depicting a stylised black-clad oarsman holding a gold medal in one hand. He presented them to the rowers after the final.
"I said to him, 'Bloody hell, Don, you were cheeky to get those printed.' He said, 'Weebs if you haven't won they'd never have seen the light of day.'"
In the months that followed, the stickers found their way to cars, changing rooms, hotels and toilet walls around the rowing world.
At a recent 1960s rowing reunion, there was plenty of happy talk about the return of the eights.
"The way I see it, it's an opportunity to put young people in a boat who would otherwise be lost to the sport," Veldman said.
Now, with a solid base in smaller boats, a healthy pool of talent and funding in place, Rowing NZ has recognised exactly that point.