Reading Wikipedia to find which theories are (or were) the alternatives which assumed that principle not to hold:
"The strong equivalence principle": "The first part is a version of the weak equivalence principle" "The second part is the Einstein equivalence principle (with the same definition of "local"), restated to allow gravitational experiments and self-gravitating bodies."
"This is the only form of the equivalence principle that applies to self-gravitating objects (such as stars), which have substantial internal gravitational interactions. It requires that the gravitational constant be the same everywhere in the universe and is incompatible with a fifth force. It is much more restrictive than the Einstein equivalence principle."
"Einstein's theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans–Dicke theory, satisfy only the Einstein equivalence principle." (1)
So it seems that "Brans–Dicke theory" and similar are ruled out by this observation, that is that the following line from one Wikipedia page can't remain:
"At present, both Brans–Dicke theory and general relativity are generally held to be in agreement with observation."(2)
But note that the authors of (0) don't claim that the alternative is completely impossible, but that they have measured even bigger space where the "strong equivalence principle" holds, compared to all measured up to now:
"our limit on the strong-field Nordtvedt parameter, which measures violation of the universality of free fall, is a factor of ten smaller than that obtained from (weak-field) Solar System tests"(0)
That is, of course, a success, as every scientific and measured increase of "known" is. Note that other "Solar System" tests mentioned in (0) are also very new, from this year. Also: the parameter is "a factor of almost a thousand smaller than that obtained from other strong-field tests"!
The article from Nature, of course more scientific that the OP on HN (currently: from discovermagazine.com), ends with:
"Although the [scalar–tensor] theories are not completely quashed, their hopes for validity have been made that much fainter."(4)
0) https://www.nature.com/articles/s41586-018-0265-1
1) https://en.wikipedia.org/wiki/Equivalence_principle#The_stro...
2) https://en.wikipedia.org/wiki/Brans%E2%80%93Dicke_theory
3) https://journals.aps.org/prd/abstract/10.1103/PhysRevD.48.34...