For yet another account, more pure-Roman than Dionysius of Halicarnassus, Quintilian (1.6) seems to agree that Latin is close to Aeolian:
Etymologia, quae verborum originem inquirit, a Cicerone dicta est notatio, quia nomen eius apud Aristotelen invenitur "σύμβολον", quod est "nota". […] Continet autem in se multam eruditionem, sive ex Graecis orta tractemus, quae sunt plurima praecipueque Aeolica ratione, cui est sermo noster simillimus, declinata, sive…
Etymology, which investigates the origin of words, Cicero calls "notation", because the word "symbol" was found in Aristotle, which means "note". […] See, it involves quite a lot of learning, whether we're facing down [words] from Greek—which are all over the place, especially the ones derived from the Aeolian style, which is most similar to our own language, or…
Quintilian also mentions the Aeolian letter digamma (
/w/) several times, for example in 1.4:
…in his "servus" et "vulgus" Aeolicum digammon desideratur…
…in these words, "servus" and "vulgus", we long for the Aeolian digamma…
…neutro sane modo vox quam sentimus efficitur, nec inutiliter Claudius Aeolicam illam ad hos usus litteram adiecerat.
Neither version [seruos or seruus, for modern servus] properly makes the sound that we hear. Claudius did a good deed when he adopted the Aeolian letter
Ⅎ for these purposes.
(All translations mine.)
But in all these other instances, he's complaining that Latin doesn't have digamma for
/w/: he's definitely not conflating it with Latin
F, and might not have seen the connection there at all. There were other correspondences between the Latin and Greek alphabets that were seen as pure coincidence, like Latin
/p/ with Greek
F/Ϝ might have been just another one of those.