They should have beaten the USA by a rather longer street than the one measured by the 24-6 margin at the finish, while they were thanking their lucky stars and heaving deep sighs of relief after edging past Canada 19-17 last weekend.
They have now pitched up in Argentina, a rather more chastened lot than the bunch that arrived in Canada a week earlier. Of course, the squad is much rearranged, with a host of new players called in for the final two games while others left for home. I might be doing them a disservice here, but I got the distinct impression that those who were heading back after a long, hard season were not exactly distraught to be taking their leave of the tour.
Scotland's official Test record against Argentina makes for grim reading: played 13, won 4. Yet there has been a remarkable pattern to fixtures in recent years, as three of those four victories were achieved on Argentinian soil. Andy Robinson famously led his Scots to the first Test series win in the southern hemisphere in their history in 2010 when they enjoyed a 2-0 clean sweep. Honours had been shared two years earlier, when Frank Hadden was in charge, as the Pumas won the first game and Scotland recovered to take the second.
Vern Cotter, Scotland's new head coach, is not the sort of fellow who is likely to get bogged down in past results, but he might take some enjoyment from the Scotland team's Wikipedia page. The final part of it lists the names of all the men who have coached Scotland since Bill Dickinson became the first to carry the responsibility back in 1971.
It also gives their win percentages, a table that was, until recently, topped by Ian McGeechan's 1988-93 stint when the Scots won 58% of their games. Cotter's record to date stands at a satisfying 100%.
As, of course, it should, for the two games Scotland have played under him have been against sides far beneath them in the world rankings. The win against the USA nudged the Scots back into the top eight of the global table, but any sort of loss to Argentina on Friday would lead to them dropping back out. In which light, Cotter cannot afford to treat the match in Cordoba's Estadio Mario Alberto Kempes - yes, the very ground where Scotland's 1978 football World Cup campaign collapsed in ignominy as they drew with Iran and lost to Peru - as some sort of development exercise.
In fact, there is precious little case for treating any game as that over the next 15 months. In his two games in charge so far, Cotter has awarded first caps to six players. Their number included Kevin Bryce, who was chosen for the squad on the basis of two appearances as a replacement for Glasgow last season during which he amassed the grand total of 46 minutes of play, and Alex Allan, who made Bryce look like a grizzled veteran as his two outings off the bench added up to just 12 minutes.
In other words, with a World Cup looming on next year's horizon, the time for experimentation is over. As caretaker coach between the reigns of Robinson and Cotter, Scott Johnson always said that he wanted to widen the net to test as many players as possible in the international arena, and he was true to his word, having given debuts to 16 of them. Add in the six capped by Cotter and a total of 22 new players have been brought into the Test fold since Robinson stood down just more than 18 months ago. Even when you deduct the three exiles (Duncan Taylor, Kieran Low and Blair Cowan) that is a staggering number for a country with just two professional teams.
Johnson came in for some fierce criticism when he suggested he would be happy to see Scotland lose all their summer and autumn matches so long as he had more players with Test experience by the end of it. It is the kind of thing coaches tend to say these days, and a cynic might suggest that they say it to give the impression that there is some sort of masterplan or intellectual foundation to a selection process that will, inevitably, involve a mixture of guesswork and blind faith as well as any other factors.
Yet Paul Ackford, the old England lock who went on to become one of rugby's sharper critics, once said that selection is the fundamental art of coaching. The rest, he said, is "largely self-serving hokum".
Ackford made the point in relation to Robinson's stewardship of Scotland, a period in which the former coach, whose time in charge ended in ignominious defeat to Tonga, seemed almost incapable of consistency. In the three-match run through the critical last two matches of the 2011 World Cup (which were both lost) and the first game (against England) of the 2012 Six Nations, Robinson managed to pick three different captains, three different No.8s and three different scrum-halves. Madness.
Scotland achieved an unwanted first when they failed to make it to the knockout stages of that World Cup, and they would also be whitewashed in the Six Nations for the first time in eight years.
This with a group of players who, while not world-beaters, were a lot better than those results suggested. The lesson was that consistency and continuity are as important in selection as any other factor.
So, heartening as it has been to see so many players come through and prove themselves - as most have - as Test animals, it would also be a welcome development if Cotter's future selections suggested he had a pretty clear idea of what Scotland's best XV will look like.
It is all very well having competition for places, but it is better still when a coach knows his own mind and knows which players he can call on when the going gets really tough. Because, with the World Cup looming, that's exactly what's about to happen.