Unless there is a local amendment the inspector does not get a choice. The NEC allows extending existing K&T.
Quote
II. Installation 394.10 Uses Permitted. Concealed knob-and-tube wiring shall be permitted to be installed in the hollow spaces of walls and ceilings or in unfinished attics and roof spaces as provided in 394.23 only as follows:
(1)For extensions of existing installations
(2)Elsewhere by special permission
Bob Badger Construction & Maintenance Electrician Massachusetts