Maybe. But there’s also the possibility that the fossilization happens quicker than is normally thought (you mentioned fossilized skins); if that is the case then the underlying [soft]tissues may also be effectively sealed and thusly more preserved than thought. (Like, if you will, forming a can around the food.)
The biggest “patch” of fossilized skin was about 1’ square. It’s a lot more likely that this “soft” tissue, which is only found in very small amounts, requiring a microscope to see, is preserved by an accident of the way the minerals accumulate during the fossilization process i.e. an airless environment deep inside a thick mineralized bone.