The problem of commonly used reasoning of physical models by abstract math and/or even computer simulations is indeed in violation of causal hierarchy, in which formal models are always based on predicate logics, not vice-versa. Therefore if underlying model is proven logically wrong, then the whole formal derivations based on it becomes wrong as well - as the destiny of some formally brilliant - though logically missunderstood models has demonstrated clearly (hollow Earth theory, geocentric model of epicycles, interpretation of luminiferous Aether model by Michellson-Morley experiments, etc..). In Aether theory Higgs model plays no significant model of casual background, because AWT assumes, there are infinitely many levels of space-time compactification, which manifests in real world by may complex high dimensional interactions inside of complex ecosystems, like Borneo jungle or human society. Constrained string theory models of twelve or twenty six dimensions cannot be considered as ultimate causal background of Universe from practical reasons, Higgs boson background of Standard Model the less, because observable world is apparently more rich and dimensional, then these models are considering.
In addition, Higgs model is too vague to be considered seriously, because it has more then single formulations: Higgs model in classical physics is based on different phenomena, then Higgs-Anderson model in boson condensates and its technical derivation consists in a mere reshuffling of degrees of freedom by transforming the Higgs Lagrangian in a gauge-invariant manner. Well known "hierarchy problem" implies, that quantum corrections can make the mass of the Higgs particle arbitrarily large, since virtual particles with arbitrarily large energies are allowed in quantum mechanics. Therefore in my opinion physicists are just mixing various concepts and mechanisms mutually at each level of physical model derivation from phenomenological to formal one, which leads effectively in prediction of many types of Higgs bosons of different rest mass and behavior, thus making such hypothesis untestable.
We are facing this conceptual confusion clearly at the moment, when mainstream physics presents some discrete predictions about Higgs boson. Each particle that couples to the Higgs field has a Yukawa coupling, too. The mass of a fermion is proportional to its Yukawa coupling, meaning that the Higgs boson will couple to the most massive particle. This means that the most significant corrections to the Higgs mass will originate from the heaviest particles, most prominently the top quark. From Standard model follows, the product of Higgs boson Yukawa coupling to the left- and right-handed top quarks have nearly the same rest mass (173.1±1.3 GeV/c2) like those predicted for Higgs boson (178.0 ± 4.3 GeV/c2). We can compare the way, in which Higgs is supposed to be proved and detected at LHC:
And the way, in which formation of top-quark pairs was evidenced and detected already at Fermilab:
Because the observation agrees well both in Higgs mass, both in decay mechanism expected, it basically means, Higgs boson was observed already as a dilepton channel of top-quark pairs decay and no further research is necessary, investments into LHC experiments the less from perspective of evidence of this particular Higgs boson model - which indeed falsifies the above hypothesis of Nielsen & Ninomiya as well. Of course, conflict of many research interests with needs of society keeps these connections in secret more effectively, then every model of time-traveling Higgs thinkable can do. In another way, physicists didn't recognize the duality of heaviest particle of matter (top quark) and Higgs boson in similar way, in which they didn't recognize the duality of most lightweight photons and gravitational waves at the opposite side of energy density spectrum.
This stance is nothing very new in contemporary physics, which often looks for evidence at incorrect places, while neglecting or even refusing clear evidence from dual view of AWT. We can compare it to search for event horizon during travel into black hole, while it's evident from more distant/general perspective, we crossed it already. The "unsuccessful" research for luminiferous Aether, while ignoring dense Aether model is the iconic case of this confusion, but we can find many other analogies here. For example, scientists are looking for evidence of Lorentz symmetry violation and hidden dimensions by violation of gravitational law, while ignoring Casimir force, or they trying to search for gravitational waves, while filtering out noise from detectors, just because they don't understand their subject at transparent, intuitive level.
Apparently, additional cost of research and general confusion of layman society is the logical consequence of this collective ignorance, while it keeps many scientists in their safe jobs and salaries in the same way, like mysticism of Catholic Church of medieval era - so I don't believe in comprehension and subsequent atonement in real time.