I honestly don't know about privet, but both sheep and cattle eat small amounts of some poisonous plants as a tonic it seems. Ivy is well-known as an appetite stimulant when a ruminant is off its food, and yet in quantity is poisonous. Sheep in Wales eat laburnum - all the hedges are made of it - and yet it too is poisonous. Our sheep here keep some overhanging yews trimmed, but they never seem to be ill of it.
However some poisonous plants really are poisonous to some sheep - take rhododendron and Ronaldsays, for instance

I hadn't responded initially, hoping someone with firsthand experience would come along....