The Higgs mechanism for generating mass can be realized in many different ways, not just the one employed in the standard model. Theories can have multiple Higgs fields, in string theory a wide variety of scalar quantities can serve as the Higgs, and so on.
Meanwhile, what to do with the vacuum energy or zero-point energy of quantum field theory is one of the subject's outstanding problems. The leading idea still seems to be that there are numerous positive and negative contributions to the cosmological constant, and they have to cancel for anthropic reasons, but otherwise there's no particular pattern to it. But in the literature you can find numerous unlikely ideas for why the vacuum energy is cancelled or cut off or doesn't gravitate.
I mention all this as a prelude to a discussion of the curious relation mentioned in the previous post. I should mention two further things: in the standard model, it's the Higgs VEV, not the Higgs boson mass, which determines the mass scale of the other particles; and, in the standard model, the Higgs VEV and the Higgs boson mass are independent quantities, separately determined by different parameters in the Higgs potential.
Conceivably, a specific model of the Higgs field could produce a relation between Higgs VEV and Higgs boson mass. But what are we to make of a formula which relates the magnitude of the Higgs VEV to every particle with mass? And furthermore, each such particle appears exactly once, and in the same way, in the formula.
So here is today's wacky concept: (1) The zero-point energy of a quantum field is equal to the mass of one quantum of the field; (2) The sum of the squares of these energies provides the v^2 term in the Higgs potential of the standard model. Thus, it is the vacuum energy (as described by this mysterious new ansatz) which does the Higgsing.
There is a circular or bootstrap aspect to this idea, since the masses appearing in (1) are themselves supposed to be generated by yukawa couplings to this "vacuum energy" whose magnitude is a function of those masses.
I am quite aware that, even given my initial remarks about the variety of realizations of the Higgs mechanism and the various desperate ideas meant to deal with the vacuum energy problem, this is a proposal that doesn't make much sense, according to the way these concepts are normally employed. But it's the only idea I have, to explain what that formula might mean and where it could come from.
I especially regard it as significant that each massive species appears once and once only. It somehow suggests that a property of each field as a whole, rather than a property of quanta of the field, is at work here.