What made the False Incarnates what they were? Which of the seven prophecies did they fulfill in order to be called that? In the end they all failed but they must have fulfilled some part of the Nerevarine's role, otherwise they would be just Azura's servants. Does this mean they were all able to wear the Ring Moon-and-Star? Why else would their mummies be positioned around it?
My opinion (tell me if it makes sense): the Ring recognizes potential Nerevarines, including the PC. As all the failed Nerevarines received the Ring, they went and tried to fulfill their role but failed. Then the Ring was returned to the shrine, awaiting the next candidate. That would make sense, since the failed Incarnates all wore the Ring and are now its guardians.