Reference as target practice

Successful reference: You must not only hit something; you must hit the right thing. And what makes a thing the right thing is the intention of the one who refers.

I discussed this 'target practice' theory of reference a while ago. I am not impressed. The purpose of language is to communicate, and the role that reference plays is to communicate which individual the speaker is talking about. Or rather, when the speaker utters a sentence of subject-predicate form, with a referring term as subject, the purpose of reference is to communicate which individual the predicate is said to apply to.
 
So it's not just a matter of hitting the target on the bull's eye. The person you are communicating with has to understand too. How does he know you hit the target? Is it e.g. that he also has to have the target in his or her sights in some way?

We watched American Sniper over the weekend. At the target practice, there was a supervisor with binoculars who would check whether the trainee had hit the target successfully. If that is the analogy, how would it apply to reference? It implies the hearer has some privileged relationship with the target. What if the hearer is an atheist, and does not see, or refuses to see, the target? That implies an atheist cannot understand a Christian’s reference to God. But surely he can. I am sure there are a few atheists or agnostics following this discussion. Are they unable to follow it without binoculars? Surely not.