They don’t make specific promises except as a last resort because of things like 1104. I know a specific example of the feds losing a case because they granted immunity to get someone to fly to the US to testify. The witness completely blew the prosecution’s case. A federal prosecutor losing is quite the stain on their reputation. Immunity deals are the fastest way to blow a case.
The witness is supposed to say they cooperated because the law provides lighter sentences for those who cooperate voluntarily.
I think a more reasonable interpretation is “they make specific promises so frequently that there had to be a rule enacted to deal with it. I agree that you know about one case where a cooperation witness with immunity caused a problem. As to your initial claims that there is “zero chance she was offered a deal” or that any cooperation must be voluntary, we’ll have to agree to disagree.
The witness is supposed to say they cooperated because the law provides lighter sentences for those who cooperate voluntarily.