So, I am not super educated on this history, but I am the product of at least three generations of beef cattle farming. My understanding is that this phrase is true, and I think it makes some intuitive sense: if your community is based around herding cattle, stealing cattle is literally stealing the your livelihood. Furthermore, there's an "outsider" aspect to this kind of crime; it's not like there's farm A, and farm B, and farmer B steals some of A's cattle and now they have more. It's someone sneaking in from out of town, stealing your stuff, and leaving. In general, people are more likely to be lenient to their neighbors than to strangers.
I believe, if memory serves, there's a sort of racial/settler component to this as well. It ties into the whole "cowboys and indians" thing. Goes along with the whole "insider" vs "outsider" dichotomy.