Actually, about half the fan base had that reaction by the end of the episde, the other half - like me - saw the whole picture differently. AM had THE VILLIAN say those words. The lying, manipulative Russian spy. OUR HERO, Beckett, at the end of the episode said "Sophia lies alot. Sophia is not to be trusted or believed. Sophia had an agenda - which was to put doubt in the relationship between Rick and Kate. Kate didn't buy into it - and neither should we, because the villian isn't the voice of AM - it's the protagonists, our main cast. That we should be paying attention to. The villian is a voice in the world, it speaks our fears, doubts, perhaps those of the main characters, and what OUTSIDERS say. If Kate had bought into it, it would be different, but she DOESN'T - and neither does AM.
What was really important was Kate being willing to ask questions about the relationship at all. She admits her feelings and concerns to Rick several times - directly. Like when she asks, "So, how many of us are they - muses?" When Sophia says, "You know how he can be." Kate is smiling nostalgically, as opposed to Sophia's disdain.
At the end of the day Beckett knows Sophia was lying and just trying to mess with her mind. Also, yes, as you said Fairytales, there's a clear difference in the relationship Sophia described. Sophia and Castle acted on a physical attraction without really getting to know each each other. The things that annoy Sophia about Castle, Beckett has come to love and appreciate. If there's any message to take for that statement it's about why the situation doesn't apply to Caskett, and perhaps why it's good that their love story has progressed slowly. That can be looked at because Sophia's statements don't have to be TRUR in order to make the comparison.
On top of that, Castle tells her that Clara Strike may have started out like Sophia, but she changed into someone strong, caring and "kind" - someone more like Nikki Heat, more like Kate. In other words, for the 7 1/2 years before he found Kate SHE is what he'd been searching for. In one fell swoop Rick has taken away ALL of Kate's doubts about Rick's past - other muses, other women, and failed marriages - because until KATE he has never found what he was looking for. Yeah, there's a long pause and he goes "as a muse," but we know better. It's exactly the same way he said "Amazing" about the kiss in season three and then pulled it together and said, "The way you took him out, I mean." He's not talking about her as a muse, he's just talking about her, and Kate knows it.
That ending was a definite step forward. It cleared away so much of Kate's issues and insecurities about Rick, issues she's had all along, issues that came up again in Beholder. She knows now that SHE is what he's ALWAYS wanted.
Now, all she has to work on is letting herself open up and take that in, let herself BE loved by getting those walls down that have nothing to do with Rick. Part of that is going to be having to admit to Rick that she's not always strong, that she can't always deal, that she was too broken to admit the truth to him about what he said. From her perspective, now SHE is the only issue.
So, yeah, I LOVED this two-parter!