The prosecution will always run their own driving history. Is it true? Yes. The prosecution has considered your 20 year old ticket. If you wish to see if another outcome is available, you probably need to hire an attorney.
The prosecutor is wrong. You are eligible for supervision for no insurance so long as you have not had a no insurance citation in the past five years. The statute is 730 ILCS 5-6-1(g)(1). Here is a link to the statute.