Most of the jet teams know each other and admire the others, whether they ever admit it or not ... that assumes a good performance at the show, of course. If not, most people understand ONE mistake or even two. A sloppy performance means loss of respect from other team, I'd imagine. Not for the country, but for the current team and leader. All assumptions.
I competed in motorcycle observed trials for some 20 years and achieved a sate championship five times ... in my class. If I saw a good rider have bad day, I didn't lose any respect because I had bad days, too. If I saw it several times in succession, I assumed he had lost the time to practice much. If I saw it over, say, four-five trials, I assumed he had "lost the edge" and didn't keep up with current obstacle requirements. That happened when the bikes took a jump in technology. The first was the monoshock, that was looked as as a kind of "cheat" at first, but rapidly became the standard. After 2 - 3 years, if you were't riding a monoshock, you simply weren't competitive anymore.
It may not be the same in aircraft since a Folland Gnat, even today, can look VERY good in aerobatic routines if he doesn't lose track of his fuel state. The Canadian Snowbirds always put on a good show and they are flying very old airplanes.
But their show isn't in the same league as a show with, say, Sukhoi Su-37s in a show designed to showcase the performance of the Su-37. The Snowbirds are just as, or maybe more PRECISE, but don't have the capability of a Pugacev Cobra, for instance, in the their CT-114 Tutors and can't go vertical forever out of sight. They fly a great routine, but have much less than a 1 : 1 thrust-to-weight ratio. Still, precision is admired by all. The Snowbirds are very entertaining to watch live, and perform a great show.
Most people who know jet teams have always enjoyed the Frecce Tricolori team, and I love the AerMacchi 339s. The team members have a tradition of staying with the team, unlike the U.S. team that rotates assignments on a regular basis. When you REALLY get to know your teammates, you fly a very precise show, and the Frecce Tricolori definitely HAVE that reputation worldwide. Perhaps not the highest-performing airframes in the business, but VERY precise. It makes for a wonderful display.
I look forward to searching for more Italian aerobatic films after seeing your post.