I'm not sure what you mean by "eat the head off the other dog"..
Do you mean she growls, barks, or physically attacks the other dog?
Food aggression is never pretty but the mode of treating the behaviour depends on the action of the said dog and the RE-ACTION of the other dog..
No, this isn't BC behaviour. This is dog behaviour.
But its not acceptable dog behaviour.
As someone mentioned, BC's need serious mental and physical stimulation to remain healthy and happy..
You say that this dog is also people possessive of you.
This indicates to me that this dog feels she has to be Alpha leader. This is stressing her out because its really your job...(its much less stressful for a dog to let the human be the leader of the pack..but when a human doesn't step up, a dog feels he has to).
I would get her evaluated by a trainer.