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"Dance Moms" star Abby Lee Miller has come under fire after former student Nia Sioux accused Abby of being racist to her on the show ... but Abby tells TMZ although Nia has a right to freedom of speech, she remembers things differently.

Nia would've been around 10 years old when she first starred on the reality show in 2011 ... and in her memoir "Bottom of the Pyramid," she writes Abby once asked her, "Don't you just wish you had white-girl hair?" and titled Nia's first solo, "Nattie of the Jungle." The number was reportedly about a child raised by monkeys. Harper Horizon

Abby tells us ... "I have different memories compared to what the girls have. I remember doing a lot of good for them."

According to Abby, none of the kids had a contract and weren't required to sta

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