On the claims of something providing high TPS is usually just made up numbers or if even someone says they are facts they can't show proper data to prove that fact. In the end it's all just a way to promote the coin and no actual facts stated for the stats and how they came to happen. Just another part of marketing. Anything along the lines can be taken as a possible estimate than an assurity of that's what you'll get so best to check your facts before jumping the gun.
I agree somehow other resort to exaggeration and indeed a marketing scheme. Announcing anything officially should involve proper data and proven facts. It should also be tested on the main net and not just only on the test net. It must also be free of any risk or possible exploit since it is not funny for users to be exploited and hacked because of this buggy stuff. If it can not be 100% free of exploit and bugs then the simple answer is it is not possible.
This kind of data is quite hard to get. And people often does not look around for such information. There are of course some projects that claim that they have made more than 1 million TPS, which not only seem insane, but also too good to be true.
I believe this is possible but it is not yet time since I believe there are still lots of test to be done.