I think it just has to do with which meaning you ascribe to the words, “veil” and “veiling.”
The term “veil” can be used to mean a type of sheer fabric (such as the lace veiling used in a bridal veil), or it means a specific part of a nun’s habit that covers the head… or it can simply mean a length of cloth used to cover a woman’s head–which could apply to a scarf or bandana, or could even (loosely) apply to some hats I’ve seen.

It does not have to specifically mean a lace mantilla or a fancy piece of netting.
As a verb, it simply means to cover the head and/or face with cloth. Merriam-Webster also says, “to cover, provide, obscure, or conceal with or as if with a veil”. So I suspect that some are referring to one definition, and others to the other definition, and it is causing some confusion and perhaps frustration because of the differences in the use of the same word.
(FYI: “veil” is also the term used for the cloth that covers the chalice.)
HTH!