Trust Douglas Mortimer to come up with the coolest answer, ha ha (my favourite character from the Dollars films)! Great posts, thanks everyone.
In considering the question myself, I think the person or persons would have to be considerably vulnerable for me to risk my own life to go after them - children or women, etc. A cowboy had a very deep sense of personal code and reputation, the reason a gunfight could break out so quickly over a simple lack of respect or a silly insult. I remember during the research phase of writing my novel, coming across an account from a cowboy who said people were so much more respectful in those days, since insult could quickly give rise to gunplay.
I think many a young cowboy would have stepped forward or joined a posse to hunt a child stealer - after all, look what it meant to merely go up the trail for three months? Death on all sides, and not only from Indians...
Is there any doubt that cowboys were brave and courageous men (boys, actually - so also a little naive, I think). They earned almost nothing for their work.