FYI, the debate over "keeping it all together" started WITH the Apollo program, and physics/math defeated it.
But the concepts continued, and found advocates during the 1980s. In the 1990s BMDO created the Delta Clipper test vehicle.
https://www.youtube.com/watch?v=o2sHf-udJI8That used four RL10 h2/o2 engines as a proof of concept. That's where these ideas come from, they do not originate with SpaceX.
With Mars mission profiles though, I can guarantee you that the concept drawing you showed me is not feasible and the opposite of optimum. Let's just say it's ridiculous. Elon Musk is not going to open up Mars to humanity with bad ideas. But who knows, maybe someone will talk some sense into him.
I am curious, though. Why would you not see the merit in a true spacecraft, something that could loop continually between Mars and Earth? It could have artificial gravity, use ion propulsion, be extremely lightweight as it would never be stressed by gravitational fields, and in every way be optimized for deep space extended travel. As an example of this, consider that you could attach a suitable propulsion unit, and send the ISS to mars and back.
Then you would have ferry style transports at each planet.
That would have been a good question to him in that
Reddit AMA about SpaceX and Mars. Of course I see the merit, i have read about that idea before, and see it as perfectly valid. I also consider that loop ferry sort of like a moving space station. Perhaps shielding against the sun radiation bursts could be one problem, the ISS wasn't designed for that but another station/spacecraft could. If SpaceX's plan goes ahead, that very ship in the proposal could be doing the loops as well.
Almost nothing in SpaceX is original, they simply made things commercially possible after so much government stagnation. That's quite a feat, for someone who was just another geek programming in a garage like some people here, who became millionaire (by selling Paypal) and instead of sitting on his money, decided to push things for humanity realizing dreams considered "impossible" by most...