The former Scotland prop's style is an antidote to the sort of hokum and mumbo-jumbo that has become the lingua franca of rugby's professional era: no psychological games, no pointless aphorisms, no pseudo-scientific codswallop. Graham wields the straightest bat in the game.
So as he sat in the Netherdale clubhouse on Thursday evening, it was refreshing, but not exactly surprising, to hear Graham's level-headed and bluster-free assessment of Gala's 27-23 British & Irish Cup win over London Scottish last weekend. There's an awful lot of Jim Telfer in the blunt way Graham goes about his business, and the great man himself would have been nodding with satisfaction as he talked about the result.
But then, as the subject got round to what the current Gala side might go on to achieve, Graham's tone changed. His voice dropped a little, becoming almost wistful for a moment. "You know," he said, "I think this could be one of the best teams ever to come out of Gala, I really do. It's just a matter of them finding that for themselves."
The context is important here. We are sitting in a room where the walls are adorned with mementoes of Gala's past, photographs of the kind of players and kind of teams that the current side must measure up to. One has the stern faces of the class of 1971, when six Gala players were in the Scotland side that beat England at Twickenham (then did it again in the SRU centenary match at Murrayfield a week later). Another shows Jim Aitken, Peter Dods and David Leslie, the backbone of the 1984 Grand Slam side.
But Graham is serious. He was heartened by the win against London Scottish, but he wasn't particularly surprised. It is a little more than three years since he accepted an invitation from former Gala president Colin Playfair to take charge of the side which was then languishing in the second division, but he has moulded them into a team in his own image: hard-nosed, effective and honest with themselves. Now he believes they can really start doing things.
"I've read a few books about galvanising players," he explained. "If you can keep the nucleus of a group of players together for two or three seasons then you start to see the best of them. After that they know each other really well, and know what they're going to do at any given time.
"We have quite a few good players, but I don't think we have anyone who really stands out. I know that people are focusing on [fly-half] Lee Millar and [former Samoa lock] Opeta Palepoi, but they stand out because the other players let them. They all work for each other. Everyone is part of it."
Gala continue their B&I Cup campaign at Llanelli's Parc-y-Scarlets this afternoon. The game kicks off at 4.30pm, barely an hour after the Scarlets have hosted European champions Leinster in their Heineken Cup match on the same pitch. For the Gala players, it is another opportunity to breathe the same air as the game's elite, and another chance, as Graham sees it, to compare themselves against the best.
Graham said: "Players have their own perceptions of how good they think they are. I have been saying to them all week that they could ask themselves that question after the London Scottish game, just to see where they stand. I had been hammering that home all week.
"The biggest difference I know of between professional and amateur rugby players is money. Just because someone gets paid it doesn't mean he's a better rugby player than you. They get paid because it takes away the burden of having to work for a living and that allows them the time to become a better rugby player.
"Sure, you have to be a good player to get the money in the first place, but I still feel that the gap is smaller than some people think. I'm not going to, but I could rattle off the names of seven or eight players in my team who could easily make the transition, given the opportunity and maybe a year to get used to the environment."
And he should know. Even before the Union game had turned professional, Graham had moved over to rugby league, signing for Carlisle. When the XV-a-side code went open, he moved to Newcastle Falcons, belatedly winning the Scotland cap he had long coveted far more than any pay-packet. From there, he moved to a playing/coaching role with Gala, then to the Border Reivers and, finally, to the forwards coaching job with Scotland when Frank Hadden was head coach.
Many thought he had been made a scapegoat when he was sacked in 2008. Since then, his relations with Murrayfield have been virtually non-existent, a staggering state of affairs for a man with his experience, his success rate and his passion for making players better.
So was last weekend's victory a moment of vindication? In his day job in a Carlisle timber yard, does he ever yearn for a return to the big time?
"I never thought that I couldn't coach," he said. "I knew when I took the national job that it was only ever going to go one way, and that was down. But that's just part of being involved in professional sport.
"I really don't know if I would go back. It would have to be the right thing. I've said before that I would love to be involved at Newcastle at some stage, but that's not going to happen immediately because they have a great team there at the moment.
"I haven't been approached by the age-grade teams or the club international team. I would be lying if I said I never thought about it, but I'm busy as it is. If I started taking on these roles, I don't know how I would be able to manage my time. And I wouldn't want it to impact on these boys here, because this is my sole focus now.
"But if they came calling? Well, I'm a passionate Scotsman, so I would certainly help."