The IL CR is to give a credit for the tax liability in NE. Even though she is getting a refund, she may have had a tax liability. For example, earned $15,000, paid in $400 and getting a refund of $300 then there was a tax liability of $100 to be reported. If she is getting back every penny paid in, there was no liability and no need for the form.
NE instructions show the filing requirements on page 6. The job was Iowa with a false sense of NE residency. I tend to err on the side of caution since clearing things up 3 or 4 years later is harder to me. Personally, I would file them all and if there is no tax liability, you can delete the sch CR from IL.
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