What exactly is this fiberboard-looking sheathing?
The material you have there is what I was taught to call celotex. There is a manufacturer that has the same name that may have been the original maker of this product. 

It is pretty much the equivalent of loosely packed sawdust drawn into a sheet and held together by binding agents and tar, I believe on the outside surface. Research on ther internet may show it is made up of something else, never the less it is not that strong, and would not work as windbracing on its own. Many, many home have this under their siding.

It will not hold a screw, it is used for sheathing only that I am aware of in all my years. You are not screwed for having it, just like any other sheathing, you don't want it to get exposed to water, especially this stuff.