In AIM 10-1-2 Helicopter Instrument Approaches, paragraph a1 says the visibility reduction rule comes from 14 CFR Section 97.3. From what I can see, that section is just definitions. What is the AIM referencing?
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.