That doesnt mean you correctly assessed them.
Why is discrimination against a black man a fun fact?
Did you read and understand the particulars of that case?
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In August 1958 William H. Burton, an African American, entered the Eagle Coffee Shoppe, a restaurant leasing space within a parking garage operated by the Wilmington Parking Authority, and was denied service solely because of his race. The Parking Authority is a tax-exempt, private corporation created by legislative action of the City of Wilmington for the purpose of operating the city's parking facilities, and its construction projects are partially funded by contributions from the city. The Parking Authority provided the restaurant heating and gas services and maintained the premises at its own expense.
This was 1958 where if they had been a completely private entity that didn't rely on the government to pay its bills they would of been within their right to discriminate against a customer based solely on their race. Not so much today. Any way let's look at the ruling.
In a 6-3 decision authored by Justice Tom C. Clark, the Court concluded that the restaurant, as a recipient of assistance by the parking authority, benefited from the city's aid and constituted an financially integral and indispensable part of the state. As such, the Court found that the restaurant and the parking authority were so physically and financially intertwined that the private entity's conduct could be imputed to the government. Thus, it’s discrimination could be considered state action in violation of the Fourteenth Amendment.
Customers have Constitutional protections that guests on private property do not. Today it wouldn't matter if they were a private entity or not you can't deny anyone service based on their race.
It's quite obvious you didn't read them or understand the difference between customers, employees and guests.