Chebbybin, why do you think that you can disagree with the Gemara? As for your doctor and rav you do not know why the doctor was allowed lechatchila (as opposed to being driven by a goy) or why the rav thought that he could hitch. See Shemirat Shabbat k’Hilkata 32,78 that a healthy person cannot eat the leftovers of food that was cooked for a sick person on Shabbat.
Member, he ia a daat yachid.