Never heard this title "Rabbi of rabbis"
Neither have I, but here's how I imagine it came about.
To an outsider, any frum Yid dressed with a hat, jacket (or Kapota) and beard is a Rabbi. Reporter comes to 770 and asks someone in the crowd who the Rebbe is, to which the response is "he's the Rebbe", reporter follows up with question "what does that mean? Is that like Rabbi?", person from the crowd answers "he's the Rabbi of everyone here".