The locals (Longsharks) are getting credit regardless of our choice.
This is just about how Mathilde's part is to be described. I.e., should Mathilde just be left out (Handing 100% to the Longsharks), or does she want them to say anything about her. This option would basically be "In Cooperation with the Empire" with a bit of flavour text about how Solidarity and Unity will always defeat the Infighting Chaos.
They are getting half the credit, we can give them all the credit and give some good will, or give that credit to an organization whose patron god Mathilde disdains. Also I think you are vastly overestimating how inspired the average citizen of Talbeheim will be over this. It is not going to be 'yay witch hunters', but more 'good that they were there this time, but I really do not like the thought of those Sigmarite foreigners muscling in'.