Not true considering you need to bring that extra fuel up in the first place, so you need a lot more fuel just to carry the weight of the descent fuel into space. It is a really tricky cost/benefit equation, but Musk seems to have figured that out.
The material cost of the fuel is something like $200k, which is peanuts for what launches as a whole usually cost. They cut into their payload to orbit budget to bring more fuel along to return with, but doing so allows them to reuse all the hardware which is the actually expensive part.
Once you are able to re-use the hardware then the cost to orbit can be lowered, which means that the 10% payload cut you took earlier actually isn't all that expensive in the first place.
That does assume that the hardware can be reused without significant refurbishing. The extensive maintenance needed due to damage incurred each flight was one reason the reusable shuttle ended up with a much higher per-launch cost than the expendable Soyuz. One can surely do much better than the shuttle, but cheap expendable systems are not that easy to beat with a reusable vehicle.
The Shuttle was a political football that had extreme requirements placed on it that were never used as part of its subsequently-shelved military mission. The Shuttle also pushed the envelope extremely hard. Finally, its funding was cut severely during development. All of this made it much less reusable than it might have been.
The SpaceX project suffers from none of these problems. A relatively conventional rocket with medium-performance engines, no crazy DoD requirements, and a sane budgeting process should do a whole lot better when it comes down to being actually reusable.
Re-using without massive refurbish costs is their ultimate goal, hence the assumption. If things go according to their plan, they are going to have turn-around of single-digit hours. Avoiding massive refurb is one of the reasons why they are not keen on dropping their rockets into salt-water for several hours. The Shuttle SRBs were really only nominally reusable. SpaceX is going for actually reusable.
A Falcon 9 lower stage also isn't a spaceplane covered in very expensive and fragile tiles, sitting next to a rocket. That helps.
Just using the first-stage without significant refurbishing will bring costs down like 50%. SpaceX has already tested their rocket engines for multiple (long) firings, but I don't know how much they refurbished them.
Yep. Once it's 'just' fuel, it's like flying a 747 across the ocean (maybe not in steerage, but chartering one), rather than building a vehicle and throwing it away. It's a 2+ order of magnitude difference, which should change things significantly.
If I remember correctly, they carry more fuel than they need in the first stage as a safety reserve, and the plan is to use that reserve fuel to land the stage. So they actually don't pay an extra weight cost, they simply make use of margin they were including anyway. If they end up having to use their safety margin, then the rocket can't land, but in the majority of flights where things run smoothly, they get to land it.
Not true considering you need to bring that extra fuel up in the first place, so you need a lot more fuel just to carry the weight of the descent fuel into space. It is a really tricky cost/benefit equation, but Musk seems to have figured that out.