About the question 'Can the mind mind affect the brain?': Some responses are 'no' because the mind is a physical 'thing' or structure (if I read it correctly). Yet if the Mind is only a physical structure why couldn't the mind affect the brain if they are both physical systems? The brain, the physical system regarding active neural excitation events and the mind, the physical system dealing with the manipulation and organization of 'established' patterns of neural-signalling. The 'higher-level' organization of the physical system, the mind, could manipulate or alter the physical system called the brain.
The question that you are referring to is worded in a way that I think is leading to the confusion. The question in the title is "Can the mind affect the brain?" but in the question body the final question posed is "Does [a thought producing a tear] not contradict the (physical) law of cause and effect?".
The answer is yes to the title question: the mind can affect the brain. The answer is no to the question posed in the body: it is not a contradiction of the law of cause and effect because the mind is a physical entity.
So you are exactly right, that the two are mutually interactive.