I think emotions often do arise from non-cognitive parts of our brain, and those parts are likely influenced by our physical body.

I'm not a neuroscientist -- and am interested in opinions of those better informed than I am -- but I've read that executive function is controlled by the "upper brain" (cerebral cortex) while our baser flight/flight instincts are controlled by the "lower brain" (amygdala).

While most of us think that the executive part of the brain is always in control, in practice we are very much influenced by the lower brain, especially in conflict situations -- we have instinctive responses around whether a person is someone to nurture, to attack or to run away from. And this is all occurring at sub-executive levels.

In couples counselling, the goal is often to mitigate interpersonal conflict by employing techniques to quickly move the interaction from the "lower brain" (fight/flight) to "upper brain" (executive function). The usual techniques prescribed are to slow things down by mirroring the other person's words (i.e. restating and asking if they got it right), validating them without agreeing, etc. By doing this, the interaction turns from an antagonistic one to a cooperative one. (I've personally tried applying these techniques to heated online discussions and have had some success).

This might also explain why when folks are under stress or under threat, their executive function is impaired -- possibly the brain is spending all of its "budget" on the lower brain.