I don't know. It is a temporary situation. The parent may need to get permission from LA for them to be homeschooled elsewhere, if it has not already been done. However, I do not think the aunt necessarily needs to get permission from her state.
The requirements for homeschooling in MS are not particularly stringent, I don't think, and I believe they'd already done what they needed to do to get it going. So most folks just said 'go for it'!