In fact, I think you're probably dead wrong. Certainly hormone interactions and feedback loops in the body have some consequence on an organism, but these things take time. Lets say that some feedback loop is extremely fast, say 10 seconds. It seems reasonable to assume that you can't have a complex feedback loop with the body much faster than that, just because it takes time for chemicals to physically move. Cognition is much, much faster than that. There are many situations where you can learn, and then apply that learning in less than a second. Now if we were instead talking about what it takes to build a complex organism that can satisfy it's own needs, then certainly these complex hormonal feedback loops are essential. You can't have an organism survive when it doesn't look for food when it's body is out of fuel or keeps eating poisonous berries because it's body can't send the reasonable feedback to it's brain, and you can forget about dropping everything and competing for mates at the correct time without some kind of behavior modifying hormonal signals!
I would say that your assertion is not significantly different from saying "you can't understand the workings of the brain without considering the complex interactions of the brain with the lungs, since without oxygen the brain can't work". So while I agree that the brain exists as part of the body, I don't see why you would automatically assume that the hormonal feedback loops with the body are at all necessary for cognition rather than a way to tell the brain when it's necessary to find food, when it's adaptive to conserve energy and be lethargic, or what have you.
My point is that we may or may not find that there is some critical ingredient of cognition hiding in this place or that, and you can't very well tell us where that will be if nobody knows if it's there.