While I've on numerous occasions received invitations to social events noting cocktail attire, I can't recall once when _black_ was specified.
I suppose, were I ever to receive such an invitation, I'd try to figure out why black was specified. If, for example, it's because the invitation's to a "Let's All Wear Black, In Support Of National Black Cocktail Attire Day!!!" party, I'd choose to decline the invitation, since none of my suits are black (nor have I ever had any real desire to own a black suit - and lest anyone ask, a charcoal suit is perfectly appropriate to wear to a funeral). If there were no special reason for specifying black, then it's not impossible that I'd accept the invitation and wear a non-black suit. Still, I do respect the right of a host/hostess to establish a dress code (even if it's a dress code which I don't find personally appealing), so I'd think long and hard before showing up dressed in navy, when my invitation asks me to wear black.
As for business, generally speaking when you accept employment, you accept that your employer can establish reasonable guidelines on how you are to dress at work and at work-related functions. If my employer required that I wear only black suits to work, I'd either wear only black suits to work, or I'd find another job.
Of course, sometimes it might be worth asking for clarification from the host/hostess or employer. If, upon asking, I'm told that navy or dark grey is acceptable, then the problem's solved. This might be the case, were black specified as a sort of shorthand for "something dark and conservative, so don't show up wearing a tan suit, or a red and white seersucker suit, or anything like that."
But, as I've said, I've never received an invitation specifying black cocktail attire (different from black tie, of course), nor have I ever worked for an organization which required me to wear black suits, so I've no actual personal experience at handling such a situation.