Do I really have to fasten interior-wall electrical wire to a stud to keep it from moving?
If you continue reading NEC 334.30 you'll come to subsection (B)...


  334.30 Securing and Supporting Nonmetallic-sheathed cable shall be supported and secured by staples, cable ties, straps, hangers, or
  similar ﬁttings designed and installed so as not to damage the cable,
  at intervals not exceeding 1.4 m (4 1⁄2 ft) and within 300 mm (12 in.)
  of every outlet box. junction box, cabinet, or ﬁtting. Flat cables
  shall not be stapled on edge. Sections of cable protected from
  physical damage by raceway shall not be required to be secured within
  the raceway.
  
  (A) Horizontal Runs Through Holes and Notches. In other than
  vertical runs, cables  installed in accordance with 300.4 shall be
  considered to be supported and secured where such support does not
  exceed 1.4-m (4 1⁄2-ft) intervals and the nonmetallic-sheathed cable
  is securely fastened in place by an approved means within 300 mm (12
  in.) of each box, cabinet, conduit body, or other nonmetallicsheathed
  cable termination. 
  
  FPN: See 314.17(C) for support where nonmetallic boxes are used
  
  (B) Unsupported Cables. Nonmetallic-sheathed cable shall be permitted to be unsupported where the cable: 
  
  (1) Is ﬁshed between access points through concealed spaces in ﬁnished
  buildings or structures and supporting is impracticable. 
  
  (2) Is not more than 1.4 m (4 1 ⁄2 ft) from the last point of cable
  support to the point of connection to a luminaire or other piece of
  electrical equipment and the cable and point of connection are within
  an accessible ceiling


So if the structure is accessible, you must secure the cable. If you are fishing cable, you do not have to secure the cable. No trained mice with staplers required.