If the "striking the opponent..." thing were enforced the way you suggest, then any scramble for a fumble would have half a dozen penalties. I've never even seen it enforced for the second clause (incidental contact from another hit) but it might have been.
In scarmbles for a fumble, I could see a lot of helmet-to-helmet penalties, too, then. I don't think it really applies in that circumstance, ya know?