"sic" with "explicitly" (and other adverbs)
Solution 1:
There's nothing wrong with the sentences. It is rather an extension of usage. [sic] can mean that something is not correct in a quote (typo etc) but you could also use it to emphasize some peculiarity of the quoted text (e.g. contradictory or dubious assertions or a value that deviates heavily from the norm). By using [sic] you normally want to express that you are aware of this discrepancy and you want the reader of your text to know that you yourself find some fact or opinion somewhat shady, not convincing or maybe not trustworthy. The link between [sic] and "explicitly" derives from that. If you say that someone else explicitly said something then you imply that 1. this person really said this and believed it and 2. that it is not your interpretation but in the original text and can be verified, e.g. in the corpus of an author. By using [sic] you somewhat disavow the controversial statement.
Within the database of CliniPharm/CliniTox (https://www.vetpharm.uzh.ch/wir/varia/sic.htm) [sic] is mostly used to indicate that the immediately preceding statement or value can be found exactly like quoted in the original publication but that the validity of the info is very arguable.