Truly effective international sides, like the city itself, are not cobbled together in a day.
Which is not to remove any of the gloss from a display of strength and skill and character, merely to highlight the point - and to his credit, coach Scott Johnson made it himself - that one-off wins are not the ingredients of greatness, no matter how dramatic their seizure.
But let us not rain too heavily on the parade. Duncan Weir's last-minute drop goal may have given him a lifetime exemption from paying for his own drinks in bars where Scotland supporters are gathered, but the point to remember was that the score was thoroughly deserved.
Scotland had worked the position beautifully, creating a platform as strong as Weir's composure. Even the Italians had to concede that the scoreline after the ball had sailed between the posts was a far better reflection of the game as a whole than the numbers on offer a few moments earlier.
How easily Scottish heads could have gone down when Luciano Orquera, a wretched figure in the corresponding game last year, had slotted the conversion which nudged Italy in front with nine minutes left. The supporters, certainly, are wearily familiar with such finishes, but Scotland found the heart, determination and, ultimately, the field position that allowed Weir to grab victory.
There is probably an Italian equivalent to the French deja vu, and it was almost certainly uttered in the Italy dressing room after the game had ended. Last June, in the Castle Series Test in Pretoria, they had also had victory snatched away at the death by a Scot, Al Strokosch grabbing an improbable and dramatic try for Scotland's 30-29 win.
Just as it is worth remembering that this was Scotland's first away victory in the RBS 6 Nations championship since they denied Ireland a Triple Crown at Croke Park in 2010, it ought to be noted that last year - when they beat Italy and Ireland in successive rounds - was the first time this century that the Scots had won back-to-back matches in the tournament.
In that light, there is a massive opportunity in the meeting with France in 12 days' time. The French were dreadful against Wales on Friday, and if they repeat that performance at Murrayfield then they will lose. Against that, the criticism France have come in for from their own media and public is on a par with what the Scots copped after their Calcutta Cup loss to England, so they may well be stung into action.
Just like Scotland, you might say. The Stadio Olimpico's bowling green pitch was far better suited to the kind of fast, offloading game Scotland want to develop than the Murrayfield quagmire, but what was in the heads of the players on Saturday was just as important as anything under their feet. There was passion and belief in this performance, a spine-tingling determination to right some Calcutta Cup wrongs.
Technically, the performance was not without its shortcomings, none more apparent than Greig Laidlaw's hesitant display at scrum-half, but there was much more good than bad.
The lineout, a disaster zone against England, functioned impeccably, with Scotland recording 100% success on their own ball and pilfering a couple of Italian throws as well. Scott Lawson, the hooker who played all 80 minutes, deserves huge credit for that, although the (inevitably more conspicuous) contribution of Richie Gray could hardly be overlooked. And as Jim Hamilton was running that particular show, then he deserves dollops of praise too.
The scrum showed a vast improvement as well. At least, it did when Geoff Cross took over at tighthead from Moray Low late in the first half. Cross looked dangerously short of game time when he was brought into the Six Nations squad a few weeks ago, but his display did not suggest he might be undercooked. It was, however, one which means he will almost certainly start against France.
Having last crossed an opponent's try-line in the November Test against Japan, Scotland had played four (and a half) touchdown-free games before Alex Dunbar slashed through the Italy defence for his 54th-minute score. The wait for the next try was rather shorter, for it was just 13 minutes later that he took a pass from Chris Cusiter, who added sharpness when he took over from Laidlaw, and sprinted in for another.
If they had kept the champagne on ice in Lockerbie after David Murdoch missed out on a curling gold medal in Sochi, then Dunbar's double gave them ample reason to get the corks popping in the Dumfriesshire town. But pleasure in his achievement goes wider, for his midfield alliance with Mat Scott is starting to look like a class combination. As both players are still just 23, it might be a lasting one as well.
And yet, there had been an ominous sense of chickens coming home to roost when Tommy/Tommaso Allan, the fly-half who opted for Italy rather than Scotland, contributed 13 points in the first half. Ultimately, Italy blew their own chances of victory by making too many elementary mistakes, but they were still strong in many areas, and dangerous to the end. The wooden spoon seems to be heading for Rome, but this was no stroll in the Italian sunshine for the Scots.
Scotland reported a clean bill of health yesterday with only Alasdair Dickinson, the Edinburgh prop who had been introduced as a second-half substitute for Ryan Grant, requiring further assessment for a calf injury.