Does the explanation assume the moon is absorbing sunlight energy and than re-emitting it like a black body? Which it is, but it's also reflecting some of the sunlight directly. Is that reflected light enough to light a fire.

If you replaced the moon with a moon-diameter flat mirror and pointed it at the earth, it would light up a spot a little bigger than the moon. From the middle of that spot you could look up at the mirror and see something that looked just like the sun slightly farther away than the normal sun. Hot and bright and capable of starting a fire.

Is this a valid reasoning?

If so, then it seems you could always start a fire with reflected sunlight. You could put a small mirror on the moon, point it at a large lens on earth (and keep it pointed at that one spot), and start a fire.

Even a smooth mirrored moon-ball should work. But I'm not sure if a diffuse reflector like the real moon is enough.

Of course, the obvious method to start a fire by moonlight is to build a nice big array of silicon mooncells, and then plug my barbecue lighter into the power converter outlet.

This also explains why you could start a fire in the middle of a moonless night with the light from a single star.

By back-of-the envelope calculation I get the diameter of the magnifying glass required is the same as diameter of Earth, within an order of magnitude.

or even venus

Excellent. My first toss would be to say that lens are increasingly difficult to manufacture below a certain aperture like f/0.5.

Couldn't grazing incidence optics be used to concentrate enough photons in a small area?