Nobody has ever passed a law or established a multinational treaty decreeing what is or isn’t a letter. But there is an essentially universal convention that English has exactly 26 lettersexactly 26 letters, and those particular 26 symbols do not include the hyphen.
Your informant is, of course, welcome to use whatever definition of letter they may wish. But they are not empowered to oblige anyone else to adopt their idiosyncratic usage of the word.