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 letters](https://en.wikipedia.org/wiki/English_alphabet), 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.