Originally Posted by Guaporense
They offered to the christian king medical treatments, which implies that the muslins at least though of themselves to be more advanced in medicine.
Or that Saladin was offering a token of friendship. Baldwin was a leper - what advanced medical treatment would Saladin's physicians have had that Baldwin's did not? The offer was one of compassion, not pity. If we had a scene where doctors were bumbling about with the king's bandaging until a glorious Arab doctor with an aura of divine light glowing behind his turban stepped in, then we might have an issue. Besides, we see Baldwin's physicians in the movie who wore their turbans as fine as any other native, so I don't think that is it.
It was obviously based on the magnanimity between Richard and Saladin during the Third Crusade, when Saladin offered his physician's services in much the same way. While modern readers insert the story from Usama ibn Munqidh, there's no indication either Saladin or Richard thought this was a supplicating gesture. Just an act of chivalry with the purpose of stating 'I care about your health enough to entrust my own trusted doctor to look after you, and that I wouldn't want you to perish while I watch and do nothing.'
Baldwin even relates a story about how Balian's father recognized the symptoms of leprosy when his physicians did not during Baldwin's childhood.