She has, after all, produced Britain's first Wimbledon men's singles champion for 77 years. So when she commented last week about the disparity in the level of success between footballers in this country and individual sportspeople, and whatever the reasons for this may be, it is surely worth listening.
Murray opined that the harsh reality of life as a professional tennis player hardens these individuals up in comparison with footballers. On the tennis circuit, players must pay their own expenses, plus that of their support team. If you are not winning tennis matches, then you are not earning any money.
Tennis looks very glitzy and glamorous when you get to the upper echelons of the sport, but a minuscule percentage of players earn the sums of money that Novak Djokovic or Andy Murray accumulate throughout the course of a season. These multi-millionaires have had to fight their way up to this level by playing on the lower status Challenger circuit, in obscure locations with one man, or woman, and his/her dog watching. As a result of this onerous journey, a ferociously driven fighting spirit has been instilled within them.
Footballers, Murray suggests, have an infinitely more comfortable existence. "I sometimes wonder with football," she says. "You can probably make a decent living from being an average player. You get your income whether you play or don't play. In an individual sport, you live or die by your own performance and I sometimes wonder when I see what footballers are earning: does it take away that drive to succeed?"
This is a sweeping generalisation of course, which cannot be applied to every footballer in Scotland. But Murray has a point. Why has Scotland produced some quite astonishing individual athletes in recent years, but so few outstanding team performers? Scotland's footballers are languishing in 50th place in the world rankings, behind footballing heavyweights such as Burkina Faso and Honduras, with scarcely any players competing at the highest level. A similar situation has emerged in rugby. Scotland had just four players in the British and Irish Lions squad this summer with only one, Richie Gray, setting foot on the pitch during the Test matches, and that was for only 13 minutes.
Why are Andy Murray, Chris Hoy, Catriona Matthew, Hannah Miley and Michael Jamieson able to excel to such an extent while our team performers falter? Competing in an individual sport is the toughest sporting challenge there is. There are no hiding places, no-one to share the workload with if you're not quite on your game that day. Individual athletes must stand up and be counted every time they compete, whereas others have more of a shield provided by their team-mates.
For an individual sportsperson, every minute in training must be utilised to its maximum, every aspect of your life geared towards maximising your performance. When Murray won the US Open last year, his maiden grand slam title and a victory that had been long in the making, he celebrated not with a magnum of champagne as he would have been fully entitled to, but a glass of lemonade.
How different this is from the endless list of footballers who get into all sorts of trouble as a result of being drunk. And that's during the season. It is more likely that Fred Perry will come back from the dead than Andy Murray will be photographed drunk and disorderly during the tennis season.
There are, of course, footballers who are consummate professionals. David Weir was famously meticulous in every area of his life, enabling him to play professionally until he was 41. The worrying thing is that his professionalism appears to be the exception, rather than the rule.
Almost invariably, individual sportspeople have a fear of failure within them which continues to drive them on. It may be the fear of where their next pay-cheque comes from; this also applies to lottery-funded athletes as funding is continuously reviewed on a results basis. Or it may just be the fear of walking out into the cauldron of competition and having no protection. It is you against the world and as exhilarating as that may be, it is also terrifying.
But it is these circumstances which really separate the wheat from the chaff. When Murray saw his two-sets-to-love lead against Novak Djokovic evaporate in the US Open final last year, it was down to him and him alone to salvage the situation. Similarly, when Hoy had to break the Olympic record to win Olympic gold in 2004, there was no one there to assist him.
Judy Murray is right; we do need to instil some of that hardness into our team performers. Changing the mentality will be a slow process, but the rewards which come with it are invaluable.