So... any good story of when a NPC try to use the card of "I have a sad story and I don't want you to help because X sad reason"? Knowing well the heroes can't stop enter because they are heroes and need to help the sad thing?

I feel like Cory and Luke are going to take that as a challenge, as though she's saying they're not awesome enough to handle her problems. If she's doing that deliberately, it would be very clever on her part. ...or maybe really obvious, considering what she's just witnessed.

It's the difference between in-character and out-of-character knowledge. Rika knows that the party can probably take the villains down, and that the stakes aren't that high. But to Vivi the character, the stakes are at the top, and Crocodile is a huge jump from taking down field agents.

The real trick with a quest that seems to have no reward is how you handle the player knowledge of experience points vs. the character not knowing. Even if you get no material reward from a difficult quest you will gain experience and might gain a level in the process.