You need to continue a few verses further. It says that one, two, or three at the most may speak in tongues at a service, as long as there is an interpreter present. If there is no interpreter, the speaker should keep quiet in the church and speak to himself and God.
I have never seen this rule followed. As a matter of fact, I have never seen or heard an interpreter.
You're absolutely right. If I hadn't stopped reading the verses at that point, I would have known that.