Oh! It might cross my mind. And I may have my doubts, but equivocally know the officer ordering the shoot is wrong? I probably would not reach that conclusion. After all, a couple of guys near the outskirts of town, with a cell phone and a motorcycle, have been known to be bad guys in AFG, and the shooters are aware of that fact even if they don't see any apparent improper activity. So, maybe the officer has some other info not in their possession (a reported radio intercept, perhaps) or can see something in his field of view that the shooter cannot. In that sense, the order is not so unusual as to let the shooter make his own clear appreciation. That's all.
As for the immunity matter, I don't know what the standard is in the US. In Canada, the crown prosecutor would have to disclose in advance that he has offered immunity to some "participating" witnesses in order to secure their collaboration. To avoid this fact "colouring" their testimony, the usual practice would normally be to charge them anyway, get them to provide their testimony under oath in a sworn statement or before a court recorder and then, at the first appearance, to declare that you have no evidence to adduce - leading to the charge being dismissed against them. The defence is then provided with all these particulars and can cross examine accordingly.
I have seen cases where even after such precautions have been taken by the crown, either the witness recanted at the trial, leading to his being declared hostile and later charged with perjury, but still tainting his testimony as unreliable, or they were shown to have had a personal beef against the person they elected to testify against and their testimony was discounted anyway.