I think that this shift in meaning happened already as part of the process of borrowing from Latin.
Look at the following example use of "videlicet". This is 16th century legal Latin as used in England. The sentence captures a defamation deposition. The language of the court is Latin, but the defamation which is a key fact of the entire proceeding had occurred in English and in the interest of accuracy is recorded in English even in the court proceedings. The word "videlicet" introduces direct or semi-direct speech and that direct speech happens to be in a different language (in Middle English).
Margaria nicolson singlewoman contra agnete blenkinsop vxor Robert in causa diffamacionis videlicet hyte hoore a whipe and a era cart/ and a franc hoode/ waies me for ye my lasse wenst haue a halpeny halter for ye to goo vp gallygait & be hanged/
The very point of this legal text's existence is that it can be read. So "videre licet" can either be understood literally, as "it is permitted to see/read", or metaphorically, as "it is permitted to learn". At the same time, it is used here to introduce the concrete "defamation" that the Latin text speaks about, and so this usage of "videlicet" would best be translated as "that is to say" or "namely".
I like this example because the English direct speech begins by an interjection "hyte", which shows that the defamation is being quoted as closely as made known to the court, rather than paraphrased or grammatically connected into the Latin sentence.
When "videlicet" entered English itself (and that process had started to already in the 15th century, while the quoted Latin text is only from the 16th century), its original Latin meaning did not need to transfer. People knew "videlicet" from similar legal and academic contexts and its meaning in English was probably simply "namely" since the beginning. English speakers who understood Latin would have known its transparent etymology in Latin, but many of English speakers who spoke no Latin might even not know that the common abbreviation "viz." once stood for "videlicet", and could be content with pronouncing it "namely" or whatever they had been taught as its standard pronunciation.