Help running romex and conduit for new outlet through cold air return
Your inspector is on the right track -- burning NM in an air return is no fun!

A smoldering cable in an air return will cause the HVAC system to blithely send all that smoke throughout the house.  Hence, the NEC restricts the wiring methods usable in ductwork and plenum spaces in 300.22; since your panned-stud air return is a kind of plenum space, 300.22(C) is the specific Code citation that applies:


  (C) Other Spaces Used for Environmental Air (Plenums).
  This section shall apply to spaces not specifically fabricated for
  environmental air-handling purposes but used for air-handling
  purposes as a plenum. This section shall not apply to habitable
  rooms or areas of buildings, the prime purpose of which is not
  air handling.
  
  Informational Note No. 1: The space over a hung ceiling used
  for environmental air-handling purposes is an example of the
  type of other space to which this section applies.
  
  Informational Note No. 2: The phrase “Other Spaces Used for
  Environmental Air (Plenum)” as used in this section correlates
  with the use of the term “plenum” in NFPA 90A-2015, Standard
  for the Installation of Air-Conditioning and Ventilating Systems, and
  other mechanical codes where the plenum is used for return air
  purposes, as well as some other air-handling spaces.
  
  Exception: This section shall not apply to the joist or stud spaces of
  dwelling units where the wiring passes through such spaces perpendicular to the long dimension of such spaces.
  
  (1) Wiring Methods. The wiring methods for such other space
  shall be limited to totally enclosed, nonventilated, insulated
  busway having no provisions for plug-in connections, Type MI
  cable without an overall nonmetallic covering, Type MC cable
  without an overall nonmetallic covering, Type AC cable, or
  other factory-assembled multiconductor control or power cable
  that is specifically listed for use within an air-handling space, or
  listed prefabricated cable assemblies of metallic manufactured
  wiring systems without nonmetallic sheath. Other types of
  cables, conductors, and raceways shall be permitted to be
  installed in electrical metallic tubing, flexible metallic tubing,
  intermediate metal conduit, rigid metal conduit without an
  overall nonmetallic covering, flexible metal conduit, or, where
  accessible, surface metal raceway or metal wireway with metal
  covers.
  
  Nonmetallic cable ties and other nonmetallic cable accessories used to secure and support cables shall be listed as having
  low smoke and heat release properties.
  
  Informational Note: One method to determine low smoke and
  heat release properties is that the nonmetallic cable ties and
  other nonmetallic cable accessories exhibit a maximum peak
  optical density of 0.50 or less, an average optical density of 0.15
  or less, and a peak heat release rate of 100 kW or less when
  tested in accordance with ANSI/UL 2043-2008, Fire Test for Heat
  and Visible Smoke Release for Discrete Products and Their Accessories
  Installed in Air-Handling Spaces.
  
  (2) Cable Tray Systems. The provisions in (a) or (b) shall
  apply to the use of metallic cable tray systems in other spaces
  used for environmental air (plenums), where accessible, as
  follows:
  
  (a) Metal Cable Tray Systems. Metal cable tray systems shall
  be permitted to support the wiring methods in 300.22(C)(1).
  
  (b) Solid Side and Bottom Metal Cable Tray Systems. Solid
  side and bottom metal cable tray systems with solid metal
  covers shall be permitted to enclose wiring methods and cables,
  not already covered in 300.22(C)(1), in accordance with
  392.10(A) and (B).
  
  (3) Equipment. Electrical equipment with a metal enclosure,
  or electrical equipment with a nonmetallic enclosure listed for
  use within an air-handling space and having low smoke and
  heat release properties, and associated wiring material suitable
  for the ambient temperature shall be permitted to be installed
  in such other space unless prohibited elsewhere in this Code.
  
  Informational Note: One method to determine low smoke and
  heat release properties is that the equipment exhibits a maxi‐
  mum peak optical density of 0.50 or less, an average optical
  density of 0.15 or less, and a peak heat release rate of 100kW or
  less when tested in accordance with ANSI/UL 2043-2013, Fire
  Test for Heat and Visible Smoke Release for Discrete Products and Their
  Accessories Installed in Air-Handling Spaces.
  
  Exception: Integral fan systems shall be permitted where specifically
  identified for use within an air-handling space.


As a result, you will need to use an unjacketed, metal-clad wiring method (type AC or MC cable is probably the easiest thing to use for this) with a metal box and faceplate if you want to mount a receptacle in this air-handling stud space.