Nature is cruel, but we don't have to be.
Nature offers no mercy: predators kill, parasites feed on their hosts, and the weak often die slowly. Grandin's point is that this tells us how the natural world works, not how we should behave. Just because something happens in nature doesn't make it a model for conduct. Humans are unusual because we can notice suffering and choose to reduce it, and that ability carries a responsibility.
The line fits the career she is known for. She is an animal scientist who spent decades designing livestock-handling systems meant to keep cattle calmer and less frightened, and she has argued that people who use animals owe them a decent life and a painless death. The attribution is common and consistent with her views, though I can't point to the exact occasion she first said it. Her stance is neither sentimental nor absolutist. She accepts the world as it is and still insists on kindness within it.
In everyday life, this might mean paying attention to where your food comes from and choosing producers with real welfare standards, even when it costs a little more. It could just as well mean refusing to be harsh with a coworker simply because the office is competitive.