Well, your definition is right in its true sense. No other country allows such assistance legally. But of course there are other surgeons around the area/premises, who can sooner take over at a short notice just in case the physician incapacitated.
But the PA programs train them up for many years covering many areas of medical faculty. When they take up the specialty and trained more and more in many of the techniques by visual and hand on experience, added to their knowledge and curriculum, why not within its limitations and under the direct supervision of the physician?( because of shortage).
But there are limitations of assignment of surgical assistance by PA/NP, like minor surgeries and a few majors which are simple and not complex.
for(eg) cesarean section or tubal ligation can be assisted by them or NP but not the laparoscopy,Vaginal or abdominal hysterectomy or radical hysterectomy, or wartheim, or TOT ,VVF so on and so forth, as the 'FIRST ASSTSTANT'.
Well, it also depends upon the physician who is confident and takes up the responsibility of trusting them in their assistance, why don't we assign them a code by appending the modifier !
Thank you.