I'm sorry but no - this does not answer the question. Expansion joints and "lateral dampers" do not make the problem of a joint offset go away. In order to resist a horizontal or vertical offset of 20+ feet with the tube "remaining stationary" then the pylon must be built to allow an extra 40+ feet to account for this movement.
How, exactly, does the pylon not suffer the same design flaw as the tunnel under the use case that you yourself brought up of a horizontal or vertical offset occuring along a splay?
If each side can move the tunnel 10 feet relative to itself without breaking, you should theoretically be able to handle up to a 20 foot slip between plates. One side bends one away, the other the other way. The pylons move 20 feet relative to each other, and only 10 feet relative to the tube.
That said, my information is based on the blueprint that Elon published and I already linked to. It includes graphs showing numerical simulations of how their design is supposed to respond to earthquakes. If you have further questions, you can start with that, then download the designs that they and others have produced and do your own work.
I am not an engineer. However I do know that engineers have done exactly what I suggested and come to the conclusion that his design is feasible.
The 40 foot figure assumes that the direction of movement is unknown and that one pylon remains fixed. I suppose you could just have each pylon capable of handling 20 feet of three dimensional movement but I doubt the economics work out in favor of that option rather than choosing towers rationally.
That said, your answer is an appeal to authority. Just because a feasibility study says it is feasible does not actually make it feasible. I skimmed the document you linked and nothing in it pertains to large ground movements that would occur due to fault offset - it is all with relation to ground shaking rather than fault slip. Further, it is common knowledge, in fact, that underground structures generally perform better under ground shaking as compared to above ground structures except when the structure crosses the fault which experiences the offset. That is, tunnels work better than pylons except at the point where the large offset occurs.
I understand that you may not be an engineer. I am an engineer, with my area of expertise being in geo-structural interaction, and I am telling you that your statement about a tunnel not being feasible because of earthquakes is NOT correct. There are plenty of other reasons why a tunnel makes no sense for this job, but seismic vulnerability is not a good one. Whether his design is feasible or not is a moot point.
Secondly it is very important that the tube remain still while the pylons move relative to it. Don't forget that we have objects moving down that tube at close to the speed of sound. It doesn't take a large local kink to be a fatal problem for people inside. You really don't want that tube to move. Enough so that keeping the tube still that it is an explicit design consideration to keep it still while the pylons expand and contract for thermal reasons.
Thirdly I well know that earthquakes are generally less of problems underground than on the surface. But trading an easy problem in most places with an impossible problem at fault boundaries is hardly an improvement. That is why I have only focused on the potentially impossible problem.
Fourth, your response was just as much an appeal to authority as mine. But my appeal to authority was an appeal to authorities whose credentials are independently verifiable, whose conclusions have been put up for public comment, and which other authorities have independently questioned, criticized, and mostly verified. Your authority is based on an anonymous claim of expertise made on the internet, in a thread where you made a basic mistake about how earthquakes are measured, with no actual analysis backing it up.
You are standing on one side of the fault and you move 10 ft north. Your pylon is standing on the other side of the fault and it moves 10 ft south. The total relative movement is 20 ft. If the assumption is that all of the relative movement is accommodated at one pylon then the pylon must be able to move 20 ft in a single direction. If the direction of the fault offset is unknown then the pylon must be able to move 20 ft in all directions for a total distance of 40 ft. We appear to be talking past each other here.
My response is not an appeal to authority - I'm not saying "it's true because I'm an engineer". I walk you through the entire logical process, so you're free to agree or disagree with any of my arguments.
This conversation clearly isn't going anywhere so I will just reiterate my point and leave it at that: an above-grade structure will perform no better than a below-grade structure if the fault deformation occurs at the location where the fault crosses the alignment. This "potentially impossible problem" is a problem for both surface and underground structures and cannot be designed around from the structural side for the magnitude of displacement that can potentially occur in CA and, in the end, it is just a risk that has to be accepted or designed around from the systems standpoint. This is alluded to in your own linked documents and noted by the the statement:
"It is also likely that in the event of a severe earthquake, Hyperloop capsules would be remotely commanded to actuate their mechanical emergency braking systems."
I guess to answer your question: I'd probably believe me.
How, exactly, does the pylon not suffer the same design flaw as the tunnel under the use case that you yourself brought up of a horizontal or vertical offset occuring along a splay?