It's still possible to build up endurance even while fat, if you never got completely sedentary or if you take the time to build it back up. But if you're too fat there comes a point where physical activity starts becoming dangerous without proper guidance - and if you have that then you're probably looking into your diet too.

When I was marathon training I found that eating enough calories was a matter of meal timing, simply because I didn't have the stomach to be able to eat that much in a single sitting.

With training a total of 50 miles (80 km) per week at a body weight of 190 lbs (85 kg), that's basically 6700 calories per week of direct energy expenditure, maybe another 1000 calories of excess post-exercise energy expenditure. That's 7700 calories per week from running, which allows you to add a whole 1100 calories per day to your diet, plus the amount you'd normally need for day to day.

With intense exercise, there's a lot of room to work with.

I wasn't trying to be pedantic as such. It's just that I found fitness when I was on a path to trying to bring my body fat down to a level I was happier with. I had originally though "losing weight" was healthy, but then I read that being active is more beneficial than losing weight, so I thought I needed to include a bit of fitness training in there.

And then when I started running, to my great surprise, I found out that I loved it, and I kept running. I ended up SUPER SUPER in to running. And one of the things that I discovered was that after a period of trying to watch how much I eat, when my training peaked, I was often struggling to get enough calories to match my burn.

And I often joked to myself back then that if I'd have known I could have outrun my bad diet, I'd have started there :P

But in all seriousness, as you said, it's not possible to sustain. Age, injury, decreased training levels, eventually, something happens and your calorie burn returns to more regular levels, and then you're not outrunning it anymore