I don't think this is quite right, though it depends on exactly what you meant. The average temperature of the earth isn't constrained by its solar insolation to a value below freezing. Were its optical properties significantly different, it could be either hotter or colder.

In thermal equilibrium, every object radiates exactly as much heat power as it receives and it will seek whatever temperature causes this to happen. In a homogenous environment, this equilibrium temperature will be that of the environment regardless of the object's optical properties (assuming it is not possible to isolate it completely).

But the earth is not in a homogenous environment. It's surrounded mostly by dark sky at just a few kelvins, but a tiny fraction of the celestial sphere -- 7.6e-5 steradians -- is at 5800K. Because of this huge temperature disparity, the heat input to the earth is mainly in the visible and near IR while the heat the earth radiates to the rest of the universe is in the far IR, and the earth's optical properties at these two wavelengths can differ. (The sun and the rest of the universe are BOTH essential for evolution and life to be thermodynamically possible.)

Hoax believers get in trouble because they apply intuition from a lifetime on the earth to a very different place, space. And heat transfer in space is probably its single most counterintuitive property.