Brien K. Meehan wrote:
91.123 Compliance with ATC clearances and instructions. (b) Except in
an emergency, no person may operate an aircraft contrary to an ATC
instruction in an area in which air traffic control is exercised.

Presumably, the approaching aircraft was in Class E airspace, which is
defined as controlled airspace. Doesn't that obligate the pilot to
follow ATC instructions given to him?

No, the class D tower has no more authority in class E as he does in
class G.



Even if it were Class G airpspace, it's a de facto "area in which air
traffic control is exercised," by the fact that the tower controller is
providing service, and the regulation applies.

Nope.



... but once a pilot contacts a controller, isnt' he obligated to
comply whether he's in that controller's jurisdiction or not?

No and the class D controller shouldn't be trying to control you outside
his airspace.