I think it's more that the weeds tolerate acid conditions a lot better than most of the grasses, so if you get the pH right for the grass they'll do better. It's the most cost effective way of improving a poor pasture. We had masses of creeping buttercup, perhaps 50% coverage in one paddock. We ended up re-seeding that one.
Our paddocks were very acid so we had a load of crushed limestone spread by a contractor. Quite a lot was in quarter inch pieces and those took 18 months to disappear completely, not helped by our drought. I guess they worked as slow release.
We asked our vet who said that 48 hours was enough time to leave the pasture before putting the animals back. The horses and sheep seemed to ignore the chunks completely. They wouldn't be palatable nor poisonous in the quantities they'd ingest with the grass.
Hope that helps