| tubachick, different organizations such as CTY or TIP run yearly talent searches; middle schoolers get to take the SAT because of their participation in the talent search. They have to list the talent search sponsor as the "high school" to which to report SAT scores (and usually pay an extra fee for participating in the talent search), though they take the SAT at any high school offering it.
I'm not certain this is the case, but my understanding is that a pre-high schooler can't simply sign up for the SAT, that to take it, he/she has to go through some other organization, such as a talent search, in order to register for it. | 
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