I think the key to the low cost of BFR is that it is being designed to be completely reusable, not in the way that F9 is, but in the way an airliner is. i.e. Launch, land, refuel launch.
That certainly seems to be Musk's goal. The giveaway was when he started talking about commercial passenger flights using the BFR...
Complete reusability associated with hardware reliability over hundreds of cycles would indeed decrease costs by several orders of magnitude. It's why millions of people are able to fly around the World on a daily basis.
Now, if you get to a point where the price of placing a kilogram into space gets down to a couple hundred bucks versus $20,000 today, why limit yourself anymore?
Space operators might as well start designing satellites that weigh 100 tons instead of 5, all the while reducing manufacturing costs (as miniaturisation and weight consciousness will not be an issue anymore) and multiplying the satellite's capabilities. That might be what Musk is thinking, and why the F9 and FH wouldn't be required anymore.
But to get there, the first thing they need to address is second stage recovery. As technically challenging and impressive as first stage recovery is, it's a walk in the park compared to getting the second stage back home in one piece.
The first thing you need to get there is lots of extra fuel. But the more fuel you carry, the bigger the rocket will be overall for the same payload.
This is why F9 will never be able to recover its second stage. In order to do so, the second stage would weigh so much that you couldn't carry a payload anymore.
Enter Falcon Heavy.
This is the rocket they'll use to start attempting second stage recovery. But in order to do so, they'll probably have to limit the payload to roughly what a Falcon 9 could carry... The overall weight gain for a similar payload is financially compensated by the fact that you recover and reuse the whole rocket. This is why FH will eventually make F9 redundant - in theory.
Now, if you push that logic further, that means that a fully reusable rocket will be much heavier than a disposable one for the same payload, and that's where BFR comes in...
As impressive as SpaceX's progress has been so far, I think we are still a long way away from BFR, or even reliable first and second stage recovery and reusability with minimal refurbishment. Progress in those fields will dictate whether Musk's dream will come true.
He makes it sound easy. I suspect it won't be. I do remember him thinking that building FH will be as easy as strapping three F9s together, only for him to realize that he had been a little optimistic. I suspect the same will go for BFR.
It doesn't matter, really, as long as reality doesn't discourage him from pushing the limits.
I'll do my own airline. With Blackjack. And hookers. In fact, forget the airline.