I can't say that I agree with this. There are the productivity "influencers" who say a lot of things but don't actually live it. There is a high correlation between being a productivity based person and being successful. Most of the leaders you admire are highly productive people and employ practices to increase their productivity, they're just too busy to soapbox about it.
I suspect the "influencers" and the "productivity gurus" you two are talking about are the same people. A guru is a type of teacher -- the really productive people don't have time to teach anyone other than, at best, their successors.
Or perhaps they leveraged their success to reduce the amount of “busy” they have so as to make time to amplify the mindset or practices that helped them, because they think that can be their biggest gift to the world.