Wikipedia on Afro: "The hairstyle is created by combing the hair away from the scalp, allowing the hair to extend out from the head in a large, rounded shape, much like a halo, cloud or ball. In persons with naturally curly or straight hair, the hairstyle is typically created with the help of creams, gels or other solidifying liquids to hold the hair in place. Particularly popular in the African-American community of the late 1960s, the hairstyle is often shaped and maintained with the assistance of a wide-toothed comb colloquially known as an afro pick.
So no, black hair doesn't magically turns itself into an afro over night. It takes styling and grooming to make regular curly hair look like that. And that's why it's part of the dress code on that school.
Your assumptions about what this means are wrong, but being wrong isn't something to be ashamed of. As others have pointed out, for many black people (not all, of course, as people vary), the "natural state" of their hair is some form of afro. Those "afros" may require some work to smooth in to a pleasing, managed shape or the traditional perfect circle, but the basic, natural shape is "giant poof of hair" for many black women.
Now, I'll point out why this is important to clarify. Again, an "afro" is essentially the state that many black girl's hair will naturally form to. We aren't even talking about neglect here: it's what happens naturally for many black girls who wash, shampoo, and condition their hair regularly. Disallowing afros is effectively the same as telling many black girls that their natural hair is bad or wrong. By contrast, the hair of virtually every white girl would be fine if you simply shampooed/conditioned it regularly. I personally know many girls who do not get haircuts for months or even years, and it's fine because their basic shampooed/conditioned hair is acceptable.
This is a problem. The implications are obvious.