Hmmm. I find that "citation needed" to be a bit confusing. If it relates to the claim of prior invention, that is cited from La cifra del. Sig. Giovan Battista Bellaso right there, and David Kahn's book The Codebreakers later in the article. So the claim seems to be pretty well attributed to me.
It almost looks like its saying they want a citation for the claim that it "is now widely known as the "Vigenère cipher". I'm not sure how one would cite such a claim, and frankly if you aren't prepared to take its truth as a given, then you shouldn't be reading a wikipedia page for it. (Confused yet?)
If you go look at Bellaso's wikipedia page, it does refer to a disagreement between the two, along with some other people (not Vigenère) taking credit for Ballaso's work.
Twenty-two years later Blaise de Vigenère described another form of
autokey using a standard table primed by a single letter [Vigenère, f.
49.], which is more vulnerable than that of Bellaso’s because of its regularity. Obviously by trying as primers all the alphabet letters in
turn the cryptogram is solved after a maximum of 20 attempts.
This to me looks like its saying Vigenère's cipher is actually much worse than Bellaso's.
This isn't related to the question, but as someone interested in the history of scientific knowledge, I found this bit at the end very intriguing:
Bellaso challenged his detractors to solve some cryptograms encrypted
according to his guidelines. He also furnished the following clue to
help the solution of one of them: ‘‘The cryptogram contains the
explanation why two balls, one in iron and one in wood, dropped from a
high place will fall on the ground at the same time.’’ This is a clear
statement of the law of the free-falling bodies forty years before
Galileo. Nobody has yet solved the cryptogram, and Bellaso’s
demonstration is still unknown.
Wow! That's a cliff-hanger on the order of Fermat's Last Theorem.