shabbas 36b: Shehiya on raw food

The Rashba raises an interesting peshat question that has great ramifications in Hilchos Shehiya.
Obviously, in the first explanation of the Mishna, based on Chananya's shita, the Mishna speaks about chazara, and shehiya is allowed according to Chananya even when not garuf and katum when the food is maachal ben derusai. What about according to the other reading -- according to Chachamim, who say that the mishna speaks about shehiya, i.e. that one can only do shehiya when the oven is garuf vekatum. So in this case, can it even cooked less than מאכל בן דרוסאי?
The Rashba suggests that one problem with this suggestion is our sugya on 18b that discusses the case of the יורה cooking the dye and the gemara's אוקימתא is to remove it from the fire (עקורה וטוחה) rather than leave it on the fire and make it garuf vekatum. Thus, the Rashba suggest that ink is like food prior to מאכל בן דרוסאי. Ultimately, the Rashba decides (as do most rishonim) that according to Chachamim one may do shehiya on an item that is not even maachal ben derusai and the Shulchan Aruch seems to say this as well, though Beur Halacha quotes Rabbi Akiva Eiger to be machmir.
Based on the Gemara we previously learned at the end of the first perek, Beis Hillel allow melacha to be done on shabbas, so what would be the problem? After all, the melacha is happening by itself and by making the item garuf and katum you have removed the possibility of stoking the fire? More specifically why is the raw meat allowed while shehiya is not. For an exhaustive discussion of this, see here. But just to address this one question, in this article, Rav Gigi suggests that when the item is in mid process of cooking (even prior to מאכל בן דרוסאי) then this active accompaniment is called מיחזי כמבשל. The heter of קדירה חייתא is based on the fact after adding this raw meat, you are not watching or accompanying the cooking anymore.