I feel compelled to take issue with #3 in a nit picky way. After 0.1 hrs behind a tow plane using fuel, the next few hours of my typical glider flight don't require any fuel at all, nor is any even available. And gas balloons don't even use fuel for launch. No disagreement with the others!
JR,
Since you want to nitpick...
Gliders still need fuel to fly. Gliders are the original solar powered aircraft. They are able to obtain sustained flight due to the unequal heating of the Earth. Since the sun's energy is provided by continuous combustion of hydrogen (a fuel), the statement "nothing flies without fuel" is factual and correct.
As for gas balloons, it takes energy (fuel) to extract helium from natural gas. It takes energy (fuel) to extract hydrogen from natural gas, oil, coal, and electrolysis of water. Rule #3 still applies.
So there ...

LOL
Wayne