Alpha rolling is dangerous and not really effective. There are other, safer ways. But yes, I agree that they need to win and should definitely take the chicken.
And to answer your question, yes, I did trust him because we actually worked through the problems instead of just intimidating him and he also was never dangerous. Just some growling and occasionally a snap but he never meant harm and was always sorry afterwards. Maybe some dogs are more severe, idk.
But either way, they need to learn respect.