(Video Link)
Say a word or a short phrase to Alyssa. She'll promptly say it backwards. How does she do it? There's no preparation or complex thinking involved. She just reverses the words like she's a machine designed for that purpose. Which is probably what's actually happening.
There. Mystery solved.
-via Dave Barry
Probably a hint that she isn't picturing what she is saying first, just reversing the phonemes.
What this girl is doing is translating the word into its written representation, reversing that representation and then repeating back a pronunciation (following English pronunciation rules) of those reversed letters.
These are different operations that would recruit different parts of the brain, and I actually think what she's doing, and what it suggests about the underlying mechanisms, is much more interesting than just "saying words backwards"... though that would be pretty cool too.