The truth to this is unequivocally that diet and proper physical activity are very close to equally important.
By 'physical activity' I don't necessarily mean exercise. Many people sit for long periods of time and in furniture that is designed to let you be lazy and not keep your spine upright on your own, shoes etc affect our posture, laying down in soft beds prevents healthy turning/tossing during sleep to prevent static positions, all of that stuff violates our natural physical activity regimen which would be one of moving about, walking, mostly upright, barefoot, grounded to the earth electrically, etc.
Exercise is a specific branch of physical activity and it can be both good and bad just like with different versions of the same food (grain fed beef vs grass fed). For example, exercising while panting with your mouth open is going to severely starve your body of oxygen, cause your muscles to ache, cause you to feel like crap over extended periods of time and do pretty much nothing for you unless the only alternative was to be hospital bed-ridden or stuck in a wheel chair to let some part of your body atrophy from non-use, like legs+wheelchair.
On a grander scale, just about everything affects our health - toxic or healthy air, temperatures can affect health too (too cold vs too warm), electrical insulation or EMF pollution, toxins like lead pipes or BPA, all the way to things as simple as posture or breathing with the mouth instead of the nose, talking too much in real life can cause this if you do it improperly (people who give speeches are known to be very exhausted afterwards for example because they are in effect starving their body of oxygen).
It's usually the weakest link in this 'grand' scale that mostly decides what our health is like. For example someone who eats an ideal diet, and exercises the ideal amount, but only gets an hour of sleep each night, is not going to have a properly functioning body, but will recover much quicker than someone who is obese and sleeps enough each night (with the fat cells storing toxins from fast food).
So, in reality, Diet vs Exercise importance will shift as one or the other becomes the weakest link for the individual. The real mystery is what exactly is the best diet, and not just WHAT foods but HOW, WHEN, QUANTITY, etc. Same thing for exercise. I think it's pretty obvious that walking, jogging, or running are the ideal human exercises but factors like barefoot vs tennis shoes can be just as important as the WHAT. Factors like how you breathe when exercising, same story. Other factors like temperature and medium of exercise too (for example, swimming would be the most ideal exercise medium for people who have joint problems if it wasn't for the extremely toxic effect of chlorinated pools).