A commonly held belief among pilots is that the FARs are regulatory, while the AIM is not. Violation of a regulation in 14 CFR is punishable by the FAA, while the AIM contains mostly "good ideas" and violation of its precepts is only punishable to the extent that it rises to the level of FAR 91.13 (careless and reckless operation). The FARs must be published in the Federal Register and generally be subject to the rulemaking process, while the AIM can be updated by the FAA at any time, with no input from anyone outside the Administration.
With that background, consider a note in the AIM, at the end of section 5-4-5(l) about Fly Visual approach segments, on page 5-4-20 (page 346 of the current PDF version of the AIM):
The FAA Administrator retains the authority to approve instrument approach procedures where the pilot may not necessarily have one of the visual references specified in 14 CFR § 91.175 and related rules. It is not a function of procedure design to ensure compliance with § 91.175. The annotation “Fly Visual to Airport” provides relief from § 91.175 requirements that the pilot have distinctly visible and identifiable visual references prior to descent below MDA/DA.
This is, as far as I can tell, the only location where this exemption from FAR 91.175 is described. FAR 91.175 is quite specific in the elements needed before continuing beyond the DA/MDA, and does not stipulate that the Administrator has the authority to authorize exemptions. For an example of one that does, consider FAR 91.117(a):
Unless otherwise authorized by the Administrator, no person may operate an aircraft below 10,000 feet MSL at an indicated airspeed of more than 250 knots (288 m.p.h.).
What authority gives the AIM the ability to carve out an exception to the FARs? Are there other situations where the FARs are contradicted by a non-regulatory document without explicitly allowing exemptions or authorization by the Administrator?