I can confirm. I was preparing from marathon some years ago and the fastest improvements I have seen were when I started going for runs on empty stomach in the morning.

But, I would make sure to give all my body needs immediately after the exercise.

Runs are better as well, some Sundays I don't eat, go for a 30k run on 14:00 and have a meal after. Feels great. Never do breakfast either, sometimes lunch if I feel like it otherwise just a big meal in the evening.

I do this, but usually more by accident than anything else— I lane swim (1hr) or do a bike ride (1.5-2hrs) first thing in the morning before I've had much of a chance to eat anything, and then afterwards have a big protein shake or some bacon and eggs.

I feel like I'd be prone to cramps if I tried push myself after having eaten much.