@layman,
I don't have some vendetta against you. Earlier you made a statement that is wholly untrue. Let's leave alone whether "does" marks for number right now because it's not that important for showing why you are wrong.
You suggested that HAS in the sentence was wrong because of an implicit reference to a group. But that is not why HAS is wrong. When I saw this I didn't intervene because I knew we'd argue but when camlok made me realize that of course conjugation occurs in the auxiliary verb, I decided to step in.
Depending on the noun or pronoun in a sentence, verbs are conjugated differently. In a language like Arabic, all pronouns conjugate differently in, say, the simple present, but in English pronouns are conjugated into one of two forms--singular and plural.
Example verb: keep
I keep
she/he keeps
you keep
we keep
they keep
Keep is the plural form and keeps is the singular form.
Similarly it could be said that do is the plural form and does is the singular form, hence marking for number. (That's how I took it.)
Because anyone is grammatically singular, does instead of do must be used, because do is the plural form. That's my analysis at least.
Any one of you is not grammatically singular.
When you said the sentence needs HAVE not HAS because of an implicit reference to a group. That was wrong. If anything, the sentence needs DOES not DO because anyone is grammatically singular.