Where's this idea? Most of the farmers I know don't believe this. They know their animals have some level of intelligence. There is a huge amount of scientific attention given to livestock - from genetics and breeding, to disease, management practices, etc.
Maybe this is just what people who have never been around livestock believe?
The animals learned about the humans as well. For instance, walking to the back edge of the farm in the fall to fix fencing, the cows would change their routine to follow - especially the part were you might route through the field full of apple trees.
Sure enough, you'd see that the cows had eaten all the apples they could reach but there were vast quantities of ripe apples higher up. So you climbed the tree and used your legs to shake branches, causing bushels of apples to thunder down. The cows that had followed would call loudly to summon their herd mates, who would come at the run.
If the sheep saw me on the same trip, I'd be ignored...unless I was carrying a bucket, which meant it probably had oats, at which point I'd have a herd of sheep converging on my position.