See this video for a particularly nasty stress test of a carbon frame. Specifically note that they replaced the shock with a simple metal tube. It simulates a hard hit without any suspension (not even tires).
Generally, carbon seems to be pretty strong. The reasons that it still has (had?) a reputation to be more troublesome are these:
- It is strong in the directions intended by the maker. That is, for stresses that occur during intended use, it is fine. Anything else may not be - hence why you find a lot of discussions even about how to hang a carbon frame bike from a bike stand, or that you should not put it on top of a car. Stresses that never occur during regular use can be neglected towards a more light frame during production. This is, due to how the frames are built, not possible to the same extent, for aluminium or steel bikes, hence those tend to be less likely to be damaged by weird positions.
- It fails catastrophically - i.e., it does not bend, or develop visible fissures over a long time, but when it fails, it fails with a snap. This is, first, psychologically worse then a steel/alu bike bending, or having a visible omen a few rides before it happens; and also objectively a little bit worse - a steel/alu frame can stomach a little dent in a noncritical section; a carbon bike can't.
- It is easily damaged by screwing in screws with the wrong moment, or by using wrong lubrication. This kind of damage is trivially avoided by using proper tools, but still a psychological factor.
So the question is not whether carbon road bikes are good for offroad use, but whether road bikes are good for offroad use. And this depends solely on your riding technique. Your body weight is several times the amount of bike weight, and can be an incredibly effective spring; what you do with it matters a lot more than the material of the frame.