Rose is confirmed to be an AI, then approaches Raiden on the street.
She actually was only AI near the end when the Patriots used her image to talk to Raiden; the Colonel was always "somewhere else" and the three never met in person together.
Additionally I always interpreted her showing up right there was because of the Patriots freeing her because Raiden did what they asked and killed Solidus. The actual ending has so much imagery that a real thing like that might've been lost in the confusion