OK, but that would seem to fall under "through some other means than eating the deer". If instead of eating sick deer the wolves exiled them, or vaccinated healthy deer, presumably you'd see the same increase in deer population.
Yeah, but then there's the impact of too many deer on the forests that they browse (assuming it's a species that's a browser rather than a grazer) - when there's overpopulation, they'll eat everything they can as they grow desperate through hunger.
A forest with all the seedlings eaten out struggles to recover from the death of mature trees, which is normally an opportunity for an explosion of growth - the decaying trunk restores nutrients to the soil, the sunlight streaming through gives the seedlings an opportunity to grow as fast as they can.
So continual overpopulation ultimately leads to the head of deer a given area of forest can support dropping significantly. Predation, whether by wolves or humans, can reduce the deer population to the extent that allows the forest to recover, which in turns leads to the forest being able to sustain larger populations of deer.
