Sometimes? No you are no wrong as it rather commonplace. Indeed thats how they tend to do it here in Canada when the Government deems the population needs to be culled.
Up in the Ft MacMurray area of Northeast Alberta , the Woodland Caribou are in danger of extinction. Wolves and Caribou have co-existed up there for tens of thousands of years and the Caribou never faced extinction before. Meanwhile all of those tarsands plants are being built which strips away forests thus destroying Caribou habitat.
Rather then acknowledge it this habitat destruction that causes the population of Caribou to decline, they claim there too many wolves.
Now I grew up in both Ft Macmurray (moved there in my teens) and farmland a bit further south. While the population of wolves down in that farmland not overly great, they were there. I do not recall a single incident where a farmer lost livestock to a wolf. The wolf tended to avoid humans. In fact there was more a problem with packs of feral dogs than with Wolves. My Father and Uncles all hunted and I remember them telling me all sorts of stories of wolves. They were also farmers but would never hunt a wolf. They thought they were something special and as far as hunting went, you only hunted what you were going to eat.