Yes. A bone is a high value treat. Zack should probably eat that in his crate and be left alone. I know there are different thoughts here. I always want to be able to take anything away from my dog - if it needs to be taken away. Usually, I would practice trading my dog, by offering him something better. You don't want to just take the bone away from Zack. He growled and bit because he "thought" you were going to take it away. If you actually take it, he will think he is right.
I would probably not allow him to have the bone. No bone. Nothing to get growly about. That's just me.