That was what I was thinking too. But then they are saying electromagnetic field actually follows this "aether" like model where it interacts with photons. Now they are trying to prove that the same should be true for Higg's fields too which gives particle mass. Check the second article.
to me any meaningful theory of mass would have inertial and gravitational mass equivalence at its heart (and/or explained immediately and naturally). Higgs mass is just a theoretical workaround to provide for W,Z bosons masses. It is just a descriptive theory, i.e. "it can be thought as if it was happening that way" , i.e. any of the 1 pagers mentioned can itself replace the actual Higgs mass theory, and we'll still would have the same result, incl. that now we would be looking for and not able to find the pensils suspended in the vacuum instead of Higgs boson.