What we know for a fact, is that gas loosely held to a body like Earth, by a force like gravity, is that the gas is free to expand. There is no rigid container around the earth, holding the gas at a constant volume. When the gas is allowed to expand, then enerrgy it might trap by itself makes it expand, it doesn't make the temperature go up. You can think this out, and see how it works, its physics.

Why would what you said not be independent in any case?

Why do you believe that what you said disproves that the atmosphere is adiabatic?

BTW, "Heat from the atmosphere leaking into space" does not follow logic either, the heat in the atmosphere, has to largely stay within the atmosphere because its convected, not radiated. This is the principle of double glazing, the vacuum between the sheets of glass in double glazing is what insulates the room, the vacuum does not transmit convection heat energy, and what is space - vacuum.

What is measured reflected from a planet is just that, reflected, it never got in, the change of dielectric constant, from space to atmosphere looks like a mirror to a lot of radiated energy, this is how optic fibres work, the light is contained in the fibre by the dielectric discontiniuity betwee fibre surface, and the jacket containing the fibre (multimode fibres), or in more expensive more sophisticated fibres, the dielectric constant is varied within the fibre (Single mode fibre). Its the same reason radio waves of some frequencis bounce all around the world inside of the dielectric discontinuity between atmosphere and space, they see it like a mirror from the inside - it has nothing to do with any "greenhouse gas" effect.