From my own experience playing Counter-Strike at world-class levels, I found that, generally speaking, the best players were the most humble and down-to-earth; the ones that talked shit were not only bad teammates, but sub-par players in general. These days, I'm much better than the average Joe at first-person-shooters, but I always point out that I'm actually pretty bad: I'd get easily beaten even by mid-tier semi-pro teams. Interestingly, this is a side-effect of our human brain not quite grasping exponential growth (or log scales). Going from the 95th to the 96th percentile is much harder than going from the 50th to the 85th.
At the very top levels, everyone has very close to the same level of preparation in terms of physical training, equipment, and mental preparation. A lot of the result comes down to your mental edge on a particular day, and some luck. The mental edge is the most fickle and difficult part of the skill set, yet it is virtually everything at the top. So, everyone recognizes that they may have an on or an off day.
Recognition that just in general, a position at the top is fragile, and it is not about your previous result, but your next result, which is uncertain.
Recognition that your competitors are also extremely good and prepared, and respect for them also leads to humility.
Then, even if they've got multiple world championship seasons under their belt, they see the context of the other greats in their sport (or similar in their field).
The post-qualifying and post-race interviews in Formula 1 auto racing often provide great examples. The top qualifiers will almost always say something like: "we qualified well, we think we're prepared, and hope for a good result tomorrow.". And after winning the race, it's about the team effort and the way things fell into place to make the win. I can't recall hearing anything resembling trash-talk in that environment.
I don't know how to stop these appraisals of fake proficiency without dismantling the entire school system. There are so many students today that feel the burden of "being smart" and strive to prove it to everyone who's watching, who don't realize that they're not actually that smart, and that most people who are watching don't particularly care.
This can a tremendously valuable mindset to take up in mathematics; especially when one is a student learning under the factory model of modern school, where one is evaluated relative to their peers and the institution itself, rather than relative to the limits of what is possible. Countless "gifted and talented" students have been done a tremendous disservice by being informed at a young age by the system that they are "good at math" or "good at English" because they show relative aptitude in memorizing and regurgitating simplified models of advanced material.
Terry Tao is lucky to be so smart that he was already somewhat well-known and successful by the time he learned the truth that these administered tests of ability are arbitrary; it would be tremendously helpful for modern students to learn the same, much earlier.