I wrote the StackOverflow post, and I don't see anything in the article that points faulty assumptions.

Don't get me wrong, I am glad that someone wrote that article. I was going to write a similar one myself within a few days with all the details I didn't need to expand on in the StackOverflow question because anyone who could answer didn't need them.

If you see any specific assumption that the article points out as faulty, I would be delighted to know which. The article does not even specifically answer the specific question of whether memory-dependence-speculative execution is always canceled when a write occurs that goes to the location that was read, or it is can sometimes not be canceled when the written value coincides with the previous value. It's either one or the other. This is one assumption that we could make, or not, (we'll try not to make it if it's faulty!). But no help there. The article doesn't say.

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Something I should clarify and that may be the cause of the misunderstanding (here, or in the article if the article really points out faulty assumptions—I'm not sure it does):

It is called “constant-time programming” by tradition, but it is really “secret-independent-time-programming”, which does not roll off the tongue in the same way. Certainly, the execution time of the crucial instructions that directly handle cryptographic secrets depends on the state in which the previous instructions have left the processor. This is no big deal, because we are not trying to prove that this execution time is constant! We are only trying to prove that it does not depend on the secrets.

And we do this by proving

* that each instruction's execution time does not depend on the secret (this is what ctgrind does, with a basic but adequate set of assumptions on what the execution time of an instruction depends on. The time taken by xor eax, eax does not depend on the previous value of eax, and it doesn't matter that it is different from the time taken by xor eax, ebx. The time taken by xor eax, ebx does not depend on the values of these registers either. And so on. The only arguable chink in the ctgrind armor is integer division, which
I don't know whether Adam Langley remembered to count as having an execution time that possibly depends on the value of its arguments—as pointed out in another thread).
This works super well for symmetric cryptography. Seriously, problem solved! Now we just need to replace AES with a cipher implemented according to the new rules (the rules predate AES and the reference AES implementation does not follow them. And it would apparently be very difficult to build an AES implementation that would be efficient and that would follow the rules).

* that we can subdivide the code into subgroups of instructions such that each subgroup's execution time does not depend on the secret. This is obviously going to be necessary for perfect “constant-time” asymmetric cryptography. Most subgroups are only one instruction (phew! for these the problem is no harder than above) but a few subgroups need to have more than one. The StackOverflow question is about one such subgroup. Another subgroup is going to be the instructions that access tables in a secret-dependent way. These two non-unitary subgroups of instructions are already written in a very careful way by crypto implementers, who have been aware of the issues for some time. I am only doing a second check, questioning assumptions, and perhaps building an automatic tool for checking that an implementation does not leak information through timing when executed on current, relatively well-understood micro-architectures (better than future micro-architectures that haven't been imagined yet anyway).

“BUT THE ARTICLE SAYS ‘EXECUTION TIME’ IS A ABSTRACTION”, I hear you scream.

Yes. Define “execution time(s)” of an instruction/a group of instructions as “any observable number of cycles in the interaction between the instruction(s) and any other instructions that could be placed around it.
The goal is to make all execution times independent of all secrets. It is easy, because currently, apart from memory accesses, conditional jumps, and possibly division, all the execution times of an instruction are independent of the data it handles.