Restaurant / Diner Scene - Inaccuray?

I'm re-watching this movie after many years, and Bam! -- one thing hits me right away. Very early in the film, they have a scene with a segregated diner or restaurant -- whites-only in one section, blacks-only in another -- to try to illustrate how segregation worked. But is this even accurate?

Most documentaries that talk about civil-rights activists trying to integrate diners or restaurants in the South explain that these places wouldn't serve blacks. Black folks couldn't come in and sit down and order a meal. The most they could do was to order food for carry-out, and then stand at the end of the lunch counter and wait to receive it. Blacks weren't allowed to take a seat -- hence, the lunch counter sit-ins of the civil-rights activists in the South (starting with the sit-in at a Woolworth's lunch counter in Greensboro, North Carolina in 1960: https://en.wikipedia.org/wiki/Greensboro_sit-ins).

Looking at this scene again now, it seems very unlikely that whites in 1964 Mississippi would sit and eat in the same restaurant with blacks -- even allowing for segregated sections. But this was before my time... Can anybody shed some light on this?


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If we could see ourselves as others see us, we would vanish on the spot. - E.M. Cioran