Your hesitation to accept the interpretation on Etymonline as is may be well founded.
Some scholars (e.g., Hahn) consider the idea that the first component is from the infinitive ("scire") unsubstantiated and unlikely; for example, it could simply be the imperative "sci". See also Ernout and Meillet, Dictionnaire étymologique de la langue latine: Histoire des mots, 1932.
The original meaning of "liceo", predating "licet" = "it is allowed", was "I am for sale", i.e., it was referring to a possibility which was somehow offered, as opposed to a mere possibility which just wasn't banned by a moral, legal, or other deontic system.
Apart from "it is allowed", "licet" is also encountered in concessive constructions such as in this proverb. This is relevant because it shows us "licet" as an adverb and a word whose semantic field does not match that of the English phrase "it is allowed". (We need an adverb if we want to build on the idea that "sci-" evolved from the imperative, or from any other definite verbal form.)
I think that the English word "scilicet" can be compared to English phrases "it is good to know that [this means]..." or "it is safe/permitted/available to assume that [this means]...", and best understood as introducing a clarification or ad hoc definition. Definitions are speech acts where you perhaps don't need anybody's permission to know the definiens, but you do need to be sure that whoever used the definiendum (or a previous ambiguous phrase) really meant to define it, or to clarify it, in the way they did, or else you might misunderstand what they were stating.
The hypothetical Roman was probably in similar shoes, regardless of whether he was thinking of "scire" in "scilicet" as an imperative, infinitive, or something else altogether. They didn't need anybody's permission to learn or accept the definition, but they still depended on the speaker to define what was just said.
I'm afraid that I wasn't able to answer the question about the origin and semantic evolution of "scilicet" in Latin conclusively (unless you feel that Hahn's arguments in the reference given are entirely convincing - she calls them a proof); but I hope that I am permitted to consider your second sub-question at least half answered.