We have a head doesnt have the same implication as all people have a head. All people have a head suggests that all people possess this characteristic--a head. It's like saying every person has a head. We have a head, however, suggests that several people possess one head, if you can imagine that. I'm trying to think of a way for you to understand the suggestions of each sentence and the only thing im coming up with, which may be wrong, is that if the subject of the sentence is vague and there's little sense of quantity (eg plural pronouns), then there's room for a lot of ambiguity and misinterpretation if you don't make the object of the sentence plural to clearly show the relationship between the subject and object.