The musician in question is John Taylor of Duran Duran, and he actually makes a good (albeit not particularly original) point.
The internet has not stunted our collective musical growth, so ignore that slightly batshit comment for the moment.
However, there is unquestionably "immense power in restriction and holding back". Celebrities are celebrities because we, who are not famous, revel in watching people do things that we cannot do. You, me, and Kanye West can all post updates on Twitter. However, me and you will not appear on MTV.
Duran Duran became megacelebs because there is nothing cooler and sexier than being on TV and having your music played over video montages of the band lounging speeding yachts, throwing champagne parties, and frolicking with girls in skimpy bikinis. Of course, it was all possible because a few major labels controlled all the music, and one channel (MTV) controlled which videos were played -- when your video was in heavy rotation on MTV in 1983, EVERYONE saw it. Those times are long since gone, the industry is too fractured now. This fact seems to be lost on John Taylor.
But the question remains: given that attention spans are shrinking all the time, partly thanks to our gazes being averted to a zillion nodes in a multimedia sea, how can a musical artist seek the kind of "magnetic attraction" over that can only come with being *less* interactive with their audience? The formula has worked in dance music circles for decades (Burial, "who is Rex the Dog?", the list goes on and on). REM became exponentially more famous when they stopped touring in the early 90's and captivated music fans with two somber, emotionally draining albums accompanied by a series of unforgettable videos (this model for success is of course dead in the water now, I am simply pointing out what they did). Could the next wave of pop stars find their breakthrough by following Taylor's advice -- by finding a way to become more famous by receding from the spotlight? It would be a refreshing change ...