Oh no not that meme again.
The reason why machinists who know only a little about machining demand you must level a lathe bed or it won't work, insist on that old wives tale, is because a simple "cheap" way to prove the lathe bed isn't twisted is to simply plop a precision level on various parts of the lathe bed and various directions... If the lathe bed is level everywhere, it must be a flat plane (well, plus or minus curvature of the earth over 100 foot monsters, obviously)
Obviously machine tools don't have to be level; otherwise you'd never see them on ships, deep sea platforms, mobile "back of truck" repair trucks, things like that. They have other, somewhat more laborious or expensive ways to determine and shim flatness.
If you made the flimsiest imaginable 3-d printer, then sag might be relevant... however you're talking about beasts of a machine that can drop 10-100 rotating HP and not twist or distort... anything less than 45 degrees isn't going to matter.
Now one problem I have personally seen is some CNC gear has what boils down to a conveyor belt that streams out metal chips. So if you mounted it 10 degrees tilted, you might have chips not fall on the conveyor belt. This is usually a simple adjustment to various guards / guides / baffles. Its not a very serious concern.
As a cross industry comparison, learned helplessness is a common feature in IT/CS land, where your average luser is extremely proud to not know anything about his computer that he uses 8 hours per day, and no one expects him to know anything either. However in machine world its somewhat unusual to have IT-like levels of learned helplessness, so the average machinist dude can quite easily handle shimming a lathe or adjusting tilts and such.