Pretty much. The week before you guys found me, I asked Mr. Sheriff if the Bounties have ever had to do their work before, and he answered in the negative.

[So they're all good!]

And for reference, since I was under the impression that Jason and Natalie knew already: if we refuse, the Bandits still die one way or another, and we get to join them in death through means that Mr. Sheriff didn't specify. Unless he's feeling merciful, anyway.