The teenage Baillie's de facto school uniform at Westhill Academy near Aberdeen was a T-shirt that paid homage to the indie icons. "I had to tell people I had more than one of them," he explains. "Otherwise they would think I was a complete tramp."
Growing up in Westhill, Baillie wasn't exactly well placed to pop out and take in a gig, and when the band split in the mid-90s he reckoned that was that. "I just assumed I'd never get to see them," he goes on. "When they got back together this year, I was too busy to go to any of their gigs, and figured they would probably implode before I did get the time."
All of which only adds to the fairytale dimension of Baillie's victory, partnering Etienne Stott, in the Olympic C2 slalom event a few weeks ago. For, having pocketed his unexpected gold medal at the Lee Valley course in Hertfordshire and returned to the Olympic village in east London, Baillie was promptly invited to a party at the adidas Underground venue in Shoreditch. Guest band? You don't need to ask.
"It was another childhood dream," says Baillie, now 33. "Almost as much as winning an Olympic medal. We threw a Team GB bucket hat at the stage and Reni [the drummer] wore it for most of the evening. We were pretty chuffed about that."
Yet as strange as the experience was, it already seems almost typical of the mind-addling sequence of events that Baillie has gone through since he and Stott, last-placed of six qualifiers for the C2 final, set off first and established a time that none of their rivals could better. Pavol and Peter Hochscorner of Slovakia, undefeated in the last three Olympic finals, clipped a gate, picked up a two-second time penalty and finished third. "That's racing," says Baillie nonchalantly. "We've lost to them plenty of times."
The result upset the odds and the rankings and, even now, Baillie seems as surprised as anyone by what unfolded. "If I read a film script for what happened in the race I wouldn't believe it, it would just seem too cheesy," he explains. "But it happened.
"The interesting thing is that our run was far from perfect. Lee Valley is a very difficult place to do everything perfectly because the water is so changeable.
"We really didn't go there to win the gold medal. We went there to do our best. We were determined to run the race to our agenda and stick to what we could control. At the end of a run we knew it wasn't perfect, but nothing had gone that wrong. It had been a good, honest effort.
"We had just gone as hard as we could. We shook hands and said, well, wherever we finish that's a fair effort. When we realised we had won I was close to going into shock, but it was a nice, warm place to be."
Baillie has been in that nice, warm place ever since. For years, the focus of his sporting life has been on maintaining a level of performance that would allow his lottery funding to continue, but that life changed overnight after he picked up his gold medal. Things ought to be easier now, but he admits he isn't quite sure how.
Baillie says: "It's been strange. I've spent most of the last few weeks almost exclusively talking about myself, which made me feel a bit of a twat. But people are still asking us and they still want to hear it, and it's nice to share it because we enjoyed such amazing support, not just at the Olympics but over the last seven or eight years.
"It's pretty weird just being introduced or spoken about as an Olympic champion. It's very strange and really hard to get used to. I just seem to be dealing with emails all the time. Etienne and I are pretty unusual among the medallists because we don't have an agent, so we weren't prepared for this. We have nothing really organised.
"At the moment, we're running before we can walk with all this attention. It would be good to find the time just to talk about what we're going to do in the future, but even that has been difficult."
Baillie is on a flying visit to Scotland at the moment, catching up with his parents in Westhill. He is scheduled to make an appearance at this weekend's Bank of Scotland Great Scottish Run where he will be meeting and congratulating runners after they arrive in Glasgow Green at the Bank of Scotland's London 2012 Celebration marquee.
The trip home also allows him to check out his gold postbox. Or rather postboxes. The Royal Mail's first attempt to honour Westhill's most famous son caused a stir when they gilded a rather undistinguished box on the opposite side of town to the family home. After complaints, they remedied the situation by painting another one in the town centre.
His appointment with the Stone Roses apart, Baillie's celebrations have been a model of moderation and temperance. After his nose-to-the-grindstone preparations for the Olympics, he was perfectly prepared – and, frankly, entitled – to have a bit of a blow-out, but a hangover on the day after he collected his medal rather put him off any further indulgence.
"Funnily enough, I didn't drink nearly as heavily over the rest of the games period as I would have expected," he laughs. "If you had asked me beforehand I would have said I would be crawling about on the floor. But I felt awful that next day and that put me off a bit.
"Also, when I was out I usually had my medal with me, and you really don't want to be absolutely battered when you've got that with you. It was a sobering influence."
Does he fear the post-Olympic blues that have been predicted for Britain's medallists by past winners? Not really. "It would be nice to take a holiday and do some more easygoing stuff," he suggests. "The Olympics, especially at home, were just such a huge opportunity, so for the past 18 months there have been no compromises and no risks taken because we didn't want to regret anything.
"Going forward, I hope we can relax a little bit, maybe train in a more light-hearted way."
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