Zahavasdad,
I don’t think you meant it the way it came out, so I’ll explain where I think you misunderstood popa.
I think you understood him to mean that since we rely on Hashem, we don’t need to do organ donations. By extension, we shouldn’t need to go to doctors either, you point out, which proves the fallacy of the original assumption.
However, popa didn’t mean that we don’t do organ donations because Hashem heals anyway. He meant that we don’t do organ donations because we hold they are assur. Even if we would end up causing loss of human life, we would still follow halacha (such as in a case where avodah zarah, giluy arayos, or shfichas domim come into conflict with pikuach nefesh).
What popa is adding, however, is that he doesn’t believe that the Ribono Shel Olam will allow anybody to die as a result of His children following His rules, and that He has at His disposal any number of ways to heal someone. I agree with popa.
Popa, correct me if I misunderstood you.