Well, the argument itself is flawless because moon does reflect sunlight and does not change its temperature dramatically, so its blackbody radiation does not varies so much
Do you understand the words you are saying, and what you are responding to?
You can talk about the temperature of light. This is the temperature of a black body which will radiate that particular combination of wavelengths at those particular intensities.
These are sometimes even given names, which don't always match.
"Warm white" is for a temperature of around 3000 K. "Cool white" is closer to 7000 K. Which is kind of broken with cool white being hotter than warm white.
A perfect mirror will simply reflect the light which hits it, and so the temperature of that light wont change.
Some people then use that to claim the moon can't be reflecting sunlight because its spectrum is different.
But it isn't a perfect mirror, so there is no need for it to be perfectly the same.
There is no need for the light from the moon to be the same temperature as the light from the sun.
The separate issue, which is far more common for FEers and other conspiracy nuts, is to claim that moonlight cools objects down rather than heats them up, which would mean it would need to be fundamentally different to sunlight. But that is due to poorly controlled experiments where it is actually exposure to the night sky cooling it down.
But since you insist on pretending things are perfect, the rest of your claims are also nonsense.
We don't see the moon completely disappear during a lunar eclipse. We see it turn orange, so there is no need for its surface to cool to 2.83 K.
And baselessly asserting the number with no justification isn't helpful at all.
Especially given the contrast with what we see at night.
Are you suggesting that at night, or in a dark room, or anything like that, where things appear black, that they have magically cooled down to 2.83K? Although I assume with that math of yours, with them being much closer would mean they need to be much colder?
I assume the incorrect math you are using is based upon considering all the light, including IR and radio waves, not just visible light.
And just like all objects without an atmosphere, the temperature of the moon does vary dramatically.
Especially given any point on it will experience roughly 2 weeks of sunlight followed by 2 weeks of no sunlight.
e.g. just reading here:
https://science.nasa.gov/moon/weather-on-the-moon/It varies from 140 K to 394 K.
I would say a change where it doubles in temperature (or halves, depending on which way you look at it) is quite a dramatic variation.
And that is without going to even darker spots, like inside craters at 27 K.
And you have also contradicted yourself.
If its temperature doesn't change much, and you need it to be 2.83 K to not be visible, why can't we see the portion which isn't illuminated by the sun? Or are you trying to suggest it remains at 2.83 K or below the entire time?
And to cap it off, your claim that the argument is flawless because an alleged conclusion of it is correct, is pure BS.
Even flawed arguments can reach the correct conclusion.