3. What If Osgood Is The Curator's Companion?
Let's assume that the Curator is the Doctor. Because, well, how can you possibly include Tom Baker in a Doctor Who anniversary, and not give him back his iconic role? Osgood was constantly waiting for the Doctor to save her. In fact, she was us in the episode; the die-hard fan, even cosplaying at the special occasion. And she wasn't utterly surprised to see multiple Doctors in the same room: no "You can't imagine what I'm thinking" joke, nothing. So what if
her Doctor works in that very building? It would explain why she had his scarf. Why it wasn't the exact scarf. And again, it opens up a world of wonderful possibility. What if together, they have their own adventures?