Your understanding of civil rights and Jim Crow is so wrong it's just astounding. I suggest you start with reading the wikipedia article on Brown v. Board of Education and Jim Crow laws.
Are you implying there were a bunch of southern business owners who wanted to provide integrated service, but were unable to because of Jim Crow? That's what it sounds like, and it's so wrong it's astounding.
Surely there must have been at least a few business owners that didn't want to spend their resources on separate facilities. Otherwise the state laws which forced segregation wouldn't have been necessary.
http://en.wikipedia.org/wiki/The_Negro_Motorist_Green_Book
What mistake do I think you are making? You said: "It actually refers to the government's legal authority to mandate that privately owned businesses provide separate nut equal facilities for blacks". No law ever forced private businesses to serve blacks in the south until the civil rights act. They may have been forced to racially segregate, but no law every forced white southern business owners to serve blacks.