Isn't this a matter of interpretation? One interpretation I've seen is that there are 4 Higgs bosons, three of which are "swallowed" by 3 of the the weak-force

Isn't this a matter of interpretation? One interpretation I've seen is that there are 4 Higgs bosons, three of which are "swallowed" by 3 of the the weak-force bosons which and become the W+ W- and Z. The remaining 4th Higgs boson (the 4th degree of freedom of the Higgs field) is what we can see, together with the 4th weak-force boson, the photon, which remains massless. So I think it's reasonable to consider that the Higgs boson belongs to the weak force.