Earlier quoted context omitted.
If even the experimental approach is only 90% accurate, how do they know which 90% is accurate?
I’m not a protein crystallographer, but here’s my generalist take. We understand the physics of e.g. X-ray diffraction pretty well, so we can fit pretty decent forward models for the x-ray data given a proposed structure. The hardest task here is getting a good enough guess at the structure to optimize the physical model, and it’s my impression that people use an iterative model refinement workflow. At least that’s h…
So you "make guesses at what the phases are", the best choice is to bootstrapping these phases measured with another technique (you can introduce crystal defects that do allow you to guess at what the phases are).
Less scrupulous is to use a computer generated model, like fitting another protein "that you guess is related", then you model the electron density, take the phases of that.
In any case you take these "phase" guesses, and then apply it to your intensities, re-run the fourier transform, refine your electron densities, twiddle the location where you think the atoms, are, then repeat with your new model. This process repeats until you converge on a structure that you're happy with.
Now alarm bells should be screaming in your head right now: Yes, it's entirely possible to converge on a wrong structure, especially if you're a young up-and-comer professor seeking tenure that has no ethical problems with "suggesting" their grad students to sleep in the lab and work 100 hour weeks and willing to do slipshod work to get you tenure: https://www.sciencedirect.com/science/article/pii/S002228360...