they expect it to be as bright as if you stood on one of those LED lights

but it looked like grey

But it’s not like a night sun

FYI - "dark side of the moon" refers to the far side of the moon (that never faces Earth). Dark here has the same meaning as in dark energy: "unknown."

I have no answer to your actual question, but would also be interested.

The "dark" side of the moon is a bit of a weird thing, both linguistically and for its tidally locked orbit ^^ The moon revolves around earth at the same speed it revolves around its axis. This "tidal locking" means that it is always showing the same "face" to the Earth, so that it doesn't appear to be rotating from our perspective.

This doesn't mean that one side is always dark and the other is exposed to the sun - just that instead of days, the moon has phases! Every time the moon is not full or new, you can see a part of it is illuminated and the other isn't. So the situation of being "on the dark side of the moon" while the Earth is visible is not possible, but it is possible to only be illuminated by earthlight.