To the title itself, yeah, that's true. But I'd say your bike analogy is off.
If I'm chubby and normally sedentary and I suddenly ride my bike five miles (without falling off),
I'm going to be in pain. You could call it a negative side effect, but it's not an injury. The pain doesn't mean I shouldn't be exercising. If anything, it means I should be.
Up until recently, I drank caffeinated beverages all throughout the day. I decided I needed to quit, and it was unpleasant. I had major mental fogginess, fatigue, irritation, and emotional issues until I'd been caffeine-free for about a week. That doesn't indicate that caffeine was good for me and that I'm harming myself by not taking it.
I can't imagine going to my doctor and saying, "Excercise and a lack of soda pop are causing me negative side effects. Please prescribe something else."
But I totally agree with you about people saying "listen to your body." My body is telling me to stuff it with chicken McNuggets, French fries, soda, and fudge sundaes. I don't think I should listen to that.