One of a host of great New Zealand middle-distance runners such as Jack Lovelock, John Walker and Murray Halberg, Snell won the Olympic 800 metres title in Rome in 1960 and followed up with a stunning double of 800 and 1,500 metres golds in Tokyo four years later.
He set several world records before his retirement in 1965, eventually moving to the United States where he earned a PhD in exercise physiology before settling in Dallas, Texas.
Speaking at a news conference at the IAAF centenary celebrations in Barcelona, Snell, who will be 74 next month and was voted New Zealand's athlete of the century in 2000, was asked why he ended up settling in the U.S. after initially moving there to study.
"I was originally going to do an undergraduate degree and go back to New Zealand and be a fitness consultant," he said.
"Then I got turned on to research and after seven years New Zealand wasn't interested but the US was and I got offered a post-graduate fellowship in Dallas, got married to a Texan and that was it.
"As far as New Zealand was concerned when they made me their athlete of the 20th century they said well why is he in the US?
"I said well no one seemed interested in having my talents in New Zealand."
Snell, who drew massive crowds when he raced at home, said he was not the only successful sporting figure from New Zealand to be neglected at home.
Yachtsman Russel Coutts had been through a similar experience when he left to lead Switzerland's Alinghi to America's Cup glory by beating Team New Zealand in 2003, he added.
"New Zealand is weird in that respect," Snell said.
"They admire the results but they don't want to help you out professionally, they do it all the time.
"They did it to Russell Coutts, who then went to Switzerland and took the Cup away. I loved that."
New Zealand suffered a slump in distance running after the glory years of Snell and Walker and Snell said changes in coaching trends had contributed.
"I think New Zealand runners got away from the coaching methods that had proved successful," he said.
"The methods of my coach (Arthur Lydiard) were controversial, distance running for middle-distance runners, and I think some of the runners coming up felt it was old-fashioned.
"They weren't looking at the times apparently. I'm absolutely sure that was the main reason."
He went on to reminisce about one of the greatest moments in his career, overhauling Belgian Roger Moens to win 800 metres gold in Rome in 1960 at the age of 21.
"I've spent quite a bit of time with Roger since and he didn't consider me a serious threat which I think was the problem," Snell said.
"His mistake was running wide and he left room for me to come on the inside," he added.
"The advantage I had in Rome was that I was a success just by making the final.
"A medal would have been fantastic and of course it ended up being gold, fantastic."