You are correct. A lot can be solved by going to scripture. Scripture refers to all believers as saints, just as it refers to all believers as priests.
And the Catholic Church does not say that all believers are not saints. Perhaps re-reading the responses by Catholics to the OP would be beneficial.
TS posted:
"This is an often miscontrued view of Catholic thought. The wrong perception is that Catholics believe that a person is not a "saint" unless given that title by the Church. This is in fact wrong. Catholics believe all who believe in Jesus Christ and are conforming their life to that of Jesus Christ are indeed saints. The title Saints is significant in that the title (though not exclusive to just those people) applies to people who have extrodinarily followed in an exempliary form, Jesus teachings. They are people who's testimony are so exemplary that we should follow their example as Paul taught his students to follow his example. However, just because someone isn't afford the "Title" of "Saints" doesn't mean they are not a saint. One of the many Missions of the Church is to lead people to be Saints in all aspects of what that means."