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Regular (ie 3+ times/wk) strength-building exercise requires some extra dietary protein for muscle repair and building. I would include plyometric exercises in that category along with heavy, difficult resistance work, but not low-weight high-rep work.
On the other hand, people focusing on general fitness/endurance/conditioning exercises like cardio (ie running, swimming, elliptical, rowing, jump rope, etc), calisthenics, and isometrics do not require any dietary adjustment assuming a normal varied diet. Obviously, if you lose too much weight, try to eat a little more of everything.
People working on improving their overall fitness usually work on resistance work (weights) and general fitness on alternate days, usually about 1 hr/day. Thus they need some extra protein and fats in their diets to avoid muscle deterioration.
Some pursuers of fitness also desire weight loss/flab loss. Despite what can be read on various sites ("Ten Great Fat-Burning Exercises"), exercise has only a little to do with that. It's 90% dietary, 10% exertion. I see some pudgeballs working out with weights and doing cardio almost daily, and over months they are just as pudgy. Stronger, no doubt.
In my case (3 days pushing the resistance, plus usually 3 days of general fitness) I was losing too much weight and plateauing on my bench, squats, and deads, so had to up my protein and carbs. I had been probably too low on both. Not on purpose, just because I am not an avid eater. Since doing that, I've gained 5 or 6 lbs but my trousers are just as loose as before so it's mostly welcome muscle.
Given what you have to work with I mostly agree. However your body type and where your fat is distributed is genetic. If you are pear shaped than vigorous exercise and committed dieting will simply make you a smaller pear. If you are 'big boned' than diet and exercise will just make you skinnier and bony.