You are missing what a protein skimmer does, it has nothing to do with removing film from the surface of the water, prehaps "skimmer" is not really an appropriate name for them.
Minute organic proteins from fish waste and uneaten food dissolve into the water forming what are known as dissolved organic solids, or DOS for short. Usually in FW aquariums these are not a problem as the fish are small and regular water changes remove the DOS from the water column, in SW large regular water changes are avoided due to cost of salt and the possibilty of upsetting the system so protein skimmers which work by lifting DOS from the water column by air stripping are used, a stream of minute bubbles from a wooden air diffuser or venturi creates a light foam which rises out of the water carring toxins with it to be collecte in a cup outside of the tank.. The problems with DOS in freshwater occur when keeping heavy polluters such as big predatory fish in large tanks where 20% water changes are impractical and this is where FW protein skimmers come into play. They work in the same way as SW protein skimmers but the air is pushed into the skimmer at a far greater pressure to counter for the lower density of the water. Wet/dry filters nor any other type of bio/mechanical filter do not and cannot remove DOS from the water column in FW, they can only be successfully removed by either water changes or protein skimming. Wet/drys and bio/mechanical filters only trap larger particals of waste which are known as organic solids rather than dissolved organic solids.