Good news everyone, I met that bug again and found the issue.
As you can see from the screenshots below, the event was well sent and executed, so the issue is more subtle than that.
My mistake was using a "set fsm Texture" while my target was expecting an object (sprite). Once I set things up correctly, my FSM worked fine again.
@PlaymakerTeam, while the cause seems benign, it caused seemingly unrelated troubles like forcing sub FSMs to finish and missing actions. An error freezing the game and pointing the user to the badly configured set FSM action could save you from mysterious bug reports like mine. These might be specific to the Template workflow.
Thanks again for your help.