Why do the hours need to be signed off by an FAA Instructor?
14 CFR 61.41
Sec. 61.41 — Flight training received from flight instructors not certificated by the FAA.
(a) A person may credit flight training toward the requirements of a pilot certificate or rating issued under this part, if that person received the training from:
(1) A flight instructor of an Armed Force in a program for training military pilots of either—
(i) The United States; or
(ii) A foreign contracting State to the Convention on International Civil Aviation.
(2) A flight instructor who is authorized to give such training by the licensing authority of a foreign contracting State to the Convention on International Civil Aviation, and the flight training is given outside the United States.
(b) A flight instructor described in paragraph (a) of this section is only authorized to give endorsements to show training given.