Recently, whilst playing the 5e starter set with a fairly novice group, a player correctly guessed an NPC's motivations. She passed a wisdom check that gave her an inkling the NPC was hiding something.
The exchange went something like this: [Spoilers for Lost Mines of Phalvender, 2nd/ 3rd act]
NPC: "We can´t thank you enough for capturing Glassstaff. It's a shame you couldn't bring any of the Redbrands back in one piece."
ROGUE: I want to make a perception check (succeeds).
DM: You sense that Halia is hiding something from you.
At this point the group had become fixated that Halia was the Black Spider and so their questioning ran around her background. The rogue remained quiet for much of this and then after some time:
ROGUE: I think Halia wanted to control the Redbrands so she could take over the village.
So, the rogue guessed pretty much what the background information to the campaign said about the NPC´s motivations.
At this point I was unsure whether to award any XP or give her any feedback because although her intuition was correct there was nothing to confirm that she was right, nor did she directly question the NPC on her theory.
What is the criteria for awarding experience points in situations like this?