Some points I agree with - there are other influential people who share similar values and who themselves influenced other managers a lot - like here Bielsa, who is using similar principles, influenced Pep, who was also someone Tuchel aspired to follow. So Rangnick and Bielsa (at least by proxy) are two inspirations for Tuchel, no wonder that Tuchel's Chelsea is operating in a similar way.
Did Hasenhüttl learn from Rangnick? I'll admit that he probably was more chosen because he used a similar style than being mentored by Rangnick. Nonetheless the point stands - Rangnick inherited Hasenhüttl's Leipzig and just evolved their style softly, so it is no wonder that the style Hasenhüttl plays is similar.
Klopp actually often talked to Rangnick at the beginning of his managing career and especially due to the schedule in that season he often could see a week later what he did wrong, as Hannover for some reason played a lot of teams just the matchday after Mainz did.
That said we are arguing a bit in a vacuum here as you rightly said, because we can only assume which stats The Athletic used for their post.