Interesting, but far from a slam dunk for hawk to prevail. Female Cooper's Hawk was almost pushed off crow more than once in video. Wing feathers on bird held down appear to have been damaged prior to encounter with hawk. Same hawk grappling one of my hens or offspring in range of a harem master game cock would very soundly driven off if not injured.Crows and ravens are members of the blue jay family of birds. There is nothing magical about crows harassing hawks. However hawks (Especially Chicken Hawks) enjoy nothing more than a nice tender filet of crow. The good news is that when the cards are delt in the hawks favor a murder of crows may well provide an alternative food source for hawks, diminishing the hawk pressure on your chickens.
If you are a crow huger the following video may be hard to watch. None the less it illustrates the true relationship between crows and hawks. The flock of agitated crows eventually decides to move on because I assume that there is nothing to see.