The tightness of the braids was never in question. And one aspect or characteristic of something does not supersede the "thing" as a whole. (i.e. Tight braids, are not necessarily a different category than Braids) Whether the braids were tight or loose, they were basically the same thing, and it comes from the fact that the composition of native africans hair required more tightness in order to keep the braids in, just as the "thinner" nature of Anglo/European hair made for a less "clean" look as strands are more likely to come undone.
I'm not sayin one group or the other invented it, my point in fact was that it would be difficult to determine.