I totally believe it. We had a big coyote that showed up at the farm not long after we lost 2 calves. Thought it was him but the cows acted like it was no big deal to see him around. The rabbit population greatly decreased so okay, let him alone. 3 years with no loses and we would see him occasionally in the field with the cows. Then he was shot and we could identify him (had some odd coloring on one shoulder) when the guy was showing him off... he was not on our place when he was shot... and within a couple months, a young pair moved in and we started losing a few chickens and then a day old calf was torn open. A few days later we WATCHED a pair of coyotes harassing a cow with a new calf , didn't have a gun as we were feeding.... and were able to scare them off. Then he found 2 dead lambs that were a month old... and he got friends in with night scopes and they killed a pair one night and then 2 more big males a week later.
I truly believe the lone coyote was a deterrent and once he was gone, the balance changed.
Have had several other farmers around here tell similar stories over the years. We do not randomly shoot them, and since moving the one donkey in with the ewes this year did not lose any lambs. We still hear some coyotes but they are not bothering the sheep at this time. Wish we had that original coyote back though, we never saw or heard other ones close up when it was here.