The education space is full of scams using perceived reputation to prey on students who don't know better. The US even set up a fake university without classes https://en.wikipedia.org/wiki/University_of_Farmington and people still signed up because they couldn't tell the difference.
If you want to evaluate education quality, look at people who've gone through the system and how they're doing afterwards.
Thats not what they are doing. They are asking people that have already been to university to name 15 universities that they consider good universities. They dont have to have attended them, they dont even rank them 1-15, they just name 15. Im assuming you can see the flaw with that model - a university that EVERYONE considers 15th would rank higher than one that 99% thought was the best and 1% didnt mention.
They also have rankings based on other metrics. And even in those where the metrics are still weighted 50% with the reputation survey the US is often not even in the top 10. I think you can draw your own conclusions there.
The rankings are literally perceived reputation. All you need to do is look at where people want to go to university. And that is overwhelmingly in the US.