I'm not convinced by that sort of thing. The series and movies reworked items all the time for either similar or completely different purposes. After all the Klingon bridge was reworked into the Enterprise torpedo bay.
Now if Spock had removed a crystal for us to all see, I would say "Yes!" But he didn't. He puts the top back on and the energizers are back on-line. That's the only thing we can assume.
I realize most fans prefer to take Shane Johnson's assertion that that's the "dilithium reactor room" as the gospel, but I choose to remain open-minded if not skeptical about it. Especially since in "Elaan of Troyius," we see Scotty working with the dilithium crystal assembly with his bare hands and no rad suit.
Sorry about taking the thread off topic a bit.