>Actually I think the hawk might like to take most of the credit there.

True. That does not mean that the box does not select the hawk. For example, lets say that the boxes condition were such that only a dove could survive long enough to reproduce, or if the dove could successfully hide within the box without being detected by the hawk. Given these possibilites, the box may select the Dove, or neither, or both.

This would have been clear to you, but you snipped out the important part where I explained how the selection happened:
The perfered strategy of the environment (the box) includes everything in the environment and all their strategies. Check out game theory.