As Jurph correctly noted, Frodo did not meet the ring in Mordor. However, that lyric could make sense in Ari Steinberg's view if you think of Frodo as meeting the corruption of The One Ring.
While Frodo did inherit the ring much earlier, he had only worn it a few times, and while it began to take hold of him, it never "took" him. I think one could look at Frodo meeting the "girl so fair" as Frodo meeting the beauty of the power of the ring. In a sense, he had never experienced the ring before like he did on the slopes of Mount Doom, and therefore was meeting that aspect of the ring for the first time.