So, I read about the Irish alphabet once, and there was a phrase saying that "V" occurs in a few native words like "vácarnach" which means to quack in English. Shouldn't the letter V be in the alphabet then if it occurs in some native words?
What it means for a letter to be "in" an alphabet is in fact quite arbitrary, and often comes down to the views of the people writing the textbooks or the Unicode proposals (which might be the government or might be some independent group).
For example, some English-speakers use spelling to distinguish "coop" (where you keep chickens) from "co-op" or "coöp" (a cooperatively owned business). Shouldn't that mean ö and - are English letters, since they're used to distinguish well-attested English words? Perhaps, but most people wouldn't consider them such, even as they use them in their own writing. I've certainly never heard English-speaking children sing "hyphen" or "dash" in the alphabet song.
Conversely, & used to be considered a letter of the English alphabet. It no longer is, for pretty much arbitrary reasons; now it's a punctuation mark instead, and we no longer list it after Z when saying the alphabet, even though its function hasn't changed.