Per the AIM, Helicopter pilots may fly non-copter approaches at half the published visibility. Where is that in the FAR?
I'm not sure what source you're looking at for the FARs but the reduction is indeed there in 14 CFR 97.3:

Copter procedures means helicopter procedures, with applicable minimums as prescribed in §97.35. Helicopters may also use other
procedures prescribed in subpart C of this part and may use the
Category A minimum descent altitude (MDA), or decision altitude or
decision height (DA/DH). For other than “copter-only” approaches, the
required visibility minimum for Category I approaches may be reduced
to one-half the published visibility minimum for Category A aircraft,
but in no case may it be reduced to less than one-quarter mile
prevailing visibility, or, if reported, 1,200 feet RVR. Reduction of
visibility minima on Category II instrument approach procedures is
prohibited.