Again and again, YankelBerel, you hit the nail on the head. Gedolei hador have never pushed themselves to the forefront and promoted themselves. That is something their followers and klal Yisrael did. The Lubavicher rebbe, on the other hand, promoted himself all the time.
Just a very very minor example. When the Lubavicher rebbe came out with the idea of learning Rambam, he said he would let them know how to divide up the hakdomo etc and when to start. Then when he came up with the system the first siyum “just happened” to fall on 11 Nissan, his birthday. What a coincidence for someone who never pushed himself to the forefront.
There are better examples and proofs, but I just thought I’d mention this obvious one.