It's a little bit more complicated than just a tuning thing. I'll have to double check, but you're right none of Toyota's Atkinson engines are a true Atkinson Cycle in regard to the original design specification of that type of cycle (the original designs used a multi-link crankshaft for lack of a better terminology, while Toyota emulates the design goals that mechanical design without actually using a multi-link crankshaft).
Last I looked into it, read about it, ect. was with the Prius; so I may be out-dated/mis-remembering the data here. They way they make that an "Atkinson Cycle" is by offsetting the crank a bit, bumping up the compression really high (if I recall it was something ridiculous like 14 or 15:1), and then bleeding off the compression via valve timing (the timing is physically different if I recall, it's not just a "program it to this") to bring it to a more acceptable level of like 12:1. There's some other details that go into it than that. But essentially a 2AZ-FE is very different than a 2AZ-FXE (Hybrid, Atkinson Cycle variant), to the point that one unlucky coworker who got a mislabeled short block doing an oil consumption recall found that it won't work in place of a 2AZ-FE block.
But the engine is actually designed to be this sort of quasi-Atkinson engine that Toyota's been using for a lot of their hybrid vehicles.
I'm sure someone like [MENTION=48413]Quentin[/MENTION] would be able to make our heads explode with all the fancy details of that set-up.