I did ask her for the code referece and this is what she e-mailed back.
First you have to read article 680.42 (Spas and Hot tubs-Outdoor installations):
680.42 Outdoor Installations.
A spa or hot tub installed outdoors shall comply with the provisions of Parts I and II of this article, except as permitted in 680.42(A) and (B), that would otherwise apply to pools installed outdoors.
Read through Part II of 680 until you find 680.23 which states that it applies to all under water luminaires
Review the definition of dry niche luminaires; this is the type found in hot tubs
Read 680.23(F) which describes the branch circuit wiring methods for feeding underwater luminaires:
680.23 (F) Branch-Circuit Wiring.
(1) Wiring Methods. Branch-circuit wiring on the supply side of enclosures and junction boxes connected to conduits run to wet-niche and no-niche luminaires, and the field wiring compartments of dry-niche luminaires, shall be installed using rigid metal conduit, intermediate metal conduit, liquidtight flexible nonmetallic conduit, rigid polyvinyl chloride conduit, or reinforced thermosetting resin conduit. Where installed on buildings, electrical metallic tubing shall be permitted, and where installed within buildings, electrical nonmetallic tubing, Type MC cable, electrical metallic tubing, or Type AC cable shall be permitted. In all cases, an insulated equipment grounding conductor sized in accordance with Table 250.122 but not less than 12 AWG shall be required.
Exception: Where connecting to transformers for pool lights, liquidtight flexible metal conduit or liquidtight flexible nonmetallic conduit shall be permitted. The length shall not exceed 1.8 m (6 ft) for any one length or exceed 3.0 m (10 ft) in total length used. Liquidtight flexible nonmetallic conduit, Type B (LFNC-B), shall be permitted in lengths longer than 1.8 m (6 ft).
(2) Equipment Grounding. Through-wall lighting assemblies, wet-niche, dry-niche, or no-niche luminaires shall be connected to an insulated copper equipment grounding conductor installed with the circuit conductors. The equipment grounding conductor shall be installed without joint or splice except as permitted in (F)(2)(a) and (F)(2)(b). The equipment grounding conductor shall be sized in accordance with Table 250.122 but shall not be smaller than 12 AWG.
I have underlined the reference to "field wiring compartments" in the paragraph above, because this refutes the point you were trying to make about a direct branch circuit feed to a pool light. With hot tubs the feed is going to a field wiring compartment (the hot tub control box).
Also note above the requirement that the equipment grounding conductor for underwater luminaires is required to have an insulated equipment grounding conductor. By using NM cable, the EGC is bare copper and does not meet this requirement.
Also read 680.42(C) Interior wiring to Outdoor installations (see last sentance in this section)
(C) Interior Wiring to Outdoor Installations. In the interior of a one-family dwelling or in the interior of another building or structure associated with a one-family dwelling, any of the wiring methods recognized in Chapter 3 of this Code that contain a copper equipment grounding conductor that is insulated or enclosed within the outer sheath of the wiring method and not smaller than 12 AWG shall be permitted to be used for the connection to motor, heating, and control loads that are part of a self-contained spa or hot tub or a packaged spa or hot tub equipment assembly. Wiring to an underwater luminaire shall comply with 680.23 or 680.33.