Why does Triolet say that she is a poem?

Triolet explains that her people knew they would die soon because their planet would be destroyed. They created a poem and put their essence into it, then transmitted it into space so that the knowledge of whom they were would not be lost. However, the poem seems to work by infecting other beings and turning them into carriers of the poem too. Once they have heard it, they will not care about anything except the poem, and so will lose themselves and their lives to it. This is why she is not welcomed everywhere, and in some places is considered to be an infection that needs to be wiped out. It is possible that Triolet herself was once a different alien being with her own life, who became infected by the poem and now only thinks of herself as a poem.