Not a teacher
------
Any works with singular, plural, and uncountable nouns. It's not any that makes you have to use plural friends; it's the context.
It's a general statement similar to "She doesn't like apples". Here, it's "She doesn't have friends", and then you add any to it.
Admittedly, even though any works with singular nouns, if the noun is countable, it's usually plural with any. It's not a hard and fast rule, though.