“If they didn’t, then all his has to say is “It’s all my fault” and he goes scott-free and so does everyone else.”
Immunity does not work that way. Part of the deal is for the perp given immunity to “fully cooperate”. That means that they tell all. All the details, all the information, and the do not hold back or use the “I forgot” without being credible. If they do, a judge can revoke the immunity.
I’d bet you were right if it wasn’t the current doj.