I used the already present script for the cowl, the one attached to the very cowl itself ( TGGrayCowlScript). However, for some reason it doesn't really work. Sure, my infamy goes to 100, and may fame goes to 0, but people still recognize me as the Champion of Cyrodiil. Even the guards are willing to talk to me, only they won't talk much because of my infamy.
And when I remove it, the guards still won't talk much, as if my infamy is still above my fame (although the statistics show the correct points).
This is a bit funny. Is there a catch to Gray Cowl's script? Maybe there's another script that controls the behavior?
EDIT: I forgot, I've looked into the script and it only has OnEquip and OnUnEquip blocks. The GameMode block is only there for SI purpose, and doesn't govern anything fame-infamy or character-wise at all)