Consider the example:

public class Test {
    @Produces
    @Named("abc")
    String abc;

    @Inject
    void setA(@Named("a") String s) {
    }

    @Inject
    void setABC(@Named("abc") String s) {
    }
}

Here, injection point in method setA should not be resolved to producer field abc, and injection point in method setABC should be resolved to it. Now, both injection points are resolved to abc.