Again there`s people he doesn`t lose sleep over. That`s nothing new. But this isn`t the reason he gets a level of trust, of which I already laid it out. After all, an anti hero will not have the shinning gleaming qualities of the conventional archetype but he requires to have heroic qualities to shoulder the bigger tragedy of character. Just so, why he gave JD the chance and after it backfires and taking down the Iron Rule he
breakes away from Roy. This is development of character tragedy. Hence why at the start of Rebirth Batman keeps an eye on him again, because he fears Jason might go down the old path but he doesn`t.
And that is why Batman gives him a lease of trust.
Lease. Not card blanche. Don`t make the statement that isn`t there.