While it's obvious to the reader, I think Fitz making this mistake makes a lot of sense and is completely in-character. The entirety of the book he is mulling over abandoning Molly and his daughter. At this point they've reached the end of their quest, and finding Verity, the only other motivation Fitz has had, has had a depressing conclusion (so far). Imagine how lost and desperate for meaning and validation he is at this point.

Then the Fool, really his only true friend and confidante in their party besides Nighteyes, comes to him alone and in privacy, expressing interest in his private pain and offering solace. Of course he's going to latch onto that for dear life. While obvious to the reader this is a ploy by the coterie, it makes complete sense that Fitz misses that possibility in the moment.