Elephants are herbivores as well. It doesn't make them subject to significantly smaller predators. An elephant simply existing and moving around would be enough to stop/injure/kill a great deal of predators, most of which don't even try because they know they'd lose.

I don't believe a cow would remain stationary if pack of Chickens started picking at its legs, and the act of moving/walking/running away in a crowd of attacking chickens would likely injure and kill chickens in the process. The difference in scale is just too great.

Plus a cow under attack would likely just run away. And cows are a lot faster than chickens, look it up.