This is a rule I've often thought about in English as a native speaker. It is my observation that whenever an "effective negation," however it is worded, occurs first in a sentence or phrase, then the subject and verb must be inverted (with an auxiliary do if necessary in modern English) in order to maintain the sense of the meaning. Examples:
Never in a million years would I say anything like that.
Rarely does it snow here like it did that year.
... nor shall any person be subject for the same offence to be twice put in jeopardy of life or limb; ...
Under no circumstances is that acceptable.
For a "partial" negation, only a positive meaning is possible without the inversion:
Rarely, it snows here like it did that year.
This is to emphasize that it does snow, albeit rarely, rather than to deny that it snows more than rarely, as in the previous example.