Exactly. And when I originally saw it, it was actually arranged as:
US cop sacked for shooting
dead black man
Which emphasises the wrong construction. Although it's also the syntactically normal construction: if you see the headline "man paints blue house", you assume that the house begins blue, rather than ends up blue.
[there's also of course an ambiguity with "shooting", as the syntactic object can be the target ("cop shoots black man"), the projectile ("machine shoots tennis balls"), or often the weapon ("child shoots machinegun"), though the pedants would prefer "fire" for the third option there]
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!