Quinn's posting to Freljord seems a little sketch, to be honest. LeBlanc, last we heard, was posing as J4. With that in mind, was J4 putting Talon on a wanted poster really a mistake? LB could definitely stand to benefit from taking out him and Katarina, and using Demacia's resources to do that would be pretty good for her.
It's a pretty good plan, except the part where Quinn started asking questions and fixing things to get the right assassin. In everyone's eyes, Quinn's just saved the day and been declared a national hero... and is rewarded with a trip to Freljord, a nation not really fond of Demacia?
She's sent alone into enemy territory, and while she prefers it that way, it's a bit weird for that to be her next assignment. It's not really clear if J4 assigned her to the post or if she suggested it herself, but assessing the danger of Freljord doesn't seem like immediately necessary work.
Of course, if LB assigned her that post, it would be a pretty good win/win situation for her. As long as Quinn's in Freljord, she can't really ask questions or correct her on any more "mistaken" identities. And while Quinn has PC immunity, if somehow there were to be an unfortunate accident, Demacia would be expected to retaliate, removing troops from Noxus' border in the process and leaving them vulnerable.