To what extent is the saying ‘a healthy body means a healthy mind’ as true as it seems?

healthy body means a healthy mind

Possible points for/against a healthy body means a healthy mind

Anxiety/stress-filled life can produce inactivity/obesity/blood pressure/depression
• Exercise – de-stresses/encourages wellbeing/enables relaxation and regular sleep patterns
• Health monitoring/preventative medicine (blood pressure/cholesterol)
• Can become obsessive about health
• Health can depend on genetics
• Mind and body are separate entities
• Needs a balanced argument before making an assessment of ‘true’