"But when we looked at the records, we found he wasn't really because he was picking up the championships all through the country. When they set out to win a race, they were doing it, and that's what got me interested."
Lydiard was a journalist's dream - outspoken and prepared to criticise those in charge of athletics.
"Arthur told me the administrators were hindering rather than helping the sport progress," said Gilmour.
"He wasn't exactly tactful about his thoughts on these people."
Lydiard's outbursts put him offside with the national body, led by Harold Austad. Five of Lydiard's runners - Snell, Halberg, Barry Magee, Jeff Julian and Ray Puckett - were among the 14-strong athletics team named for the 1960 Olympics but the coach was controversially excluded in any official capacity.
"Nothing could budge him [Austad] on the question of Arthur Lydiard being added to the team," said Gilmour.
"For a while, I rang him every day - didn't work. I think we made him even more pig-headed. In the end, he wouldn't take my calls."
But the outcry was sufficient that Gilmour's newspaper, the Auckland Star, launched a public appeal to get Lydiard to Rome.
"People tossed in their pound notes and 10 shilling notes, and it grew very well. We got Arthur over there. He would have to stay outside the camp but he could be there and that might make all the difference."
Lydiard had no official accreditation and had to coach his runners through the gates of the Olympic training track. But Snell and Halberg went on to win gold in the 800m and 5000m respectively within an hour of each other in what some still consider New Zealand's greatest sporting achievement.
"Everybody suddenly wanted to know about Peter Snell, Murray Halberg. Who's this chap Lydiard? Where did he come from? Arthur had proved to the world that he actually knew what he was talking about."
Those two golds and the bronze later earned by Magee in the marathon were the only three medals New Zealand won at the Rome Olympics.
Snell went on to complete the 800m-1500m double at the 1964 Tokyo Olympics - the last man to do so - and was named New Zealand's Sportsperson of the Century.
The training methods Lydiard pioneered continue to form the basis of distance running coaching to this day.
Gilmour had a long association with Lydiard and his athletes, professionally and personally. He was one of the original Auckland Joggers along with Lydiard and future Auckland mayor Colin Kay who were part of the club's first run in 1962.
Under Lydiard's influence, Gilmour gave up smoking and took up jogging.
He collaborated and helped Lydiard write a number of training manuals and jogging philosophies which have been published in several languages.
His first book with Lydiard was Run to the Top in 1962, followed by A Clean Pair of Heels with Halberg in 1963, No Bugles No Drums with Snell in 1965 and Unstoppable with Sandra Barwick in 1993.
He wrote 23 books, including Arthur Lydiard Master Coach in 2004, Use it or Lose It with Snell in 2006 and Peter Snell from Olympian to Scientist in 2007.
Born in Dunedin in 1925, Gilmour worked from 1941 to 1986 as a journalist on newspapers throughout the country, later moving into advertising and public relations.
He retired to Milford on Auckland's North Shore and got involved in local body politics.
Gilmour died on Thursday, June 25, aged 94.