I think it is fairly obvious.
Look at how a theatre is defined:
http://en.wikipedia.org/wiki/Theater_(warfare)
Two theatres are two regions of war, which effect each other only indirectly and not directly. Whatever happens on Germany's Eastern front does not directly influence what happens on its Western front. The only dependency of one theatre to another is that whatever ressources you put into one theatre you do not have available for the other and vice versa. And of course or winning on a front influences what ressources you have at all.
For that reason it makes sense to separate responsibilities both in real life and also in the game AI. The high command (you as a player) distributes the valuable ressources accorss the theatres and the theatres make best use of it towards their goal without worrying what the other theatre does.
Notice that the same is not true for two army groups. If army groups centre and south do not coordinate, then there is a gap in the front.
So I conclude that the theatre AI works differently as any other AI. While working towards its objectives it will always look at the overall picture in its region.