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I know people who lived into late 90's who had been sedantary all life. Never heard anyone eating junk food living that old.
Living a long life is not equivalent to leading a quality life which includes the ability to move freely. While it may be possible to remain sedentary I am highly dubious of avoiding lots of aches and arthritic (or similar) conditions if one is truly sedentary. Just observe what happens to people who sit too long at work or lie down too long in a bed. Without moderate movement, the blood in the body (as with oil in a car) does not move properly and the body "rusts". The body is designed to move.
This is very hard to determine. So much depends on genetics. I know people that can eat everything in sight and gain no weight, and I know people who can look at food and gain weight. Besides that, take my father in law for example. He lived to 96, very healthy until he hit 90. He never exercised, social drinker, quit smoking in his 40's, and ate a diet full of meat cheese, potatoes, light on the fruits and vegetables. On the other hand, take Jim Fix, who was a big running advocate back in the 70's. Wrote a book that was very popular. Died of a heat attack in his 50's. Apparently a genetic heart defect.
However, I still advocate for regular exercise and healthy eating. I'm starting to feel better and some of the problems of old age are being reduced. I also have more energy.
Finally, what is considered "healthy eating" is now an open debate again. Some are advocating a return to a higher fat, diet, but with less carbs is a healthier appetite. I think they're right, as many WWII generation people ate that kind of diet and lived a long life. Today people are obese and getting bigger every year, following our "low fat diet".
OP is telling us to choose one or the other. We all know good diet + vigorous exercise is the best choice, but if we did one or the other, which is best? I'll go with person A is more of a health risk. You can't outexercise a bad diet. And as someone else said, even if you don't do vigorous exercise at all, you walk to the sofa, to work from your car, etc, so it's healthier to eat well.