Should traditional moule marinier have cream in it?
Traditional Moules a la mariniere is finished by reducing the cooking liquid until it is concentrated and then "mounting" it with butter (monter au beurre).

Mouclade is a traditional mussel preparation from the region of Bordeaux where the cooking liquid is enriched at the end with heavy cream and sometimes egg yolks, thus the reason the judges on your show were commenting that the cream was incorrect.