Typically, immunity is offered when:
1. They KNOW the player knows SOMETHING about an accusation (see the Tennessee kid in the Bruce Pearl case)
2. The school won't come clean about a accusation.
I don't have many sources, but I do know for a fact the "immunity card" is the ace card the NCAA will play in an investigation. They don't play it unless they have to and they don't play it unless they believe the school isn't cooperating.
Those shitheads also forget that one of their own squealed on us about 12 years ago. This is not some unprecedented deal, what likely happened is they suspect a severe violation took place and the school keeps giving them the runaround. If it's discovered the school/coach lied, that school/coach is in major ****.