Well probably the set is supposed to have that appearance.

Usually set bonus is reserved for complete & intentional vanity pieces made to conform to a 'set. There are tens of thousands of vanity and equipment combinations to inspire creativity and in which they are either part of the set or not part of any set. The black crown seems to be something of it's own and probably shouldn't be completing another different set (with the fact that the black crown has a different texture, different color, and doesn't have that black-purple hue like the other pieces (knowing the set has a purple glow to it)).