A ton of people are very fit with perfect nutrition and non-lifting exercise. That's not easy to do in reverse just simply picking up some weights with garbage nutrition. Fitness is not at all dependent on weight lifting. You can go live in the wild and be much more fit than some dude who goes to a gym. Look at any definition of fitness and you won't see anything about man-made weights or gyms or any of that. Having bulging muscles from lifting big (and eating perfectly) does not determine your fitness. It's just one aspect, and one that isn't actually required to show an all around fitness level.

My sister will be running marathons probably until she dies. She'll probably continue to be more fit than you or I ever will. And she's probably never lifted weights in her life.

I get that it sounds all macho but weight lifting in the gym is not at all a necessary part of being fit. Completely depends on what you're trying to accomplish.