The insurance cover is likely also discounted using that rate code. If you are not eligible for the rate code then the insurance may be invalidated. The fact that Hertz did not check your eligibility when you rented is irrelevant.
I am sure you knew full well that you were not eligible for the IBM rate but applied it anyway for a discount.
Sounds like you may be liable for the accident damages in full, since from the sounds of it you are 100% at fault in the accident. In future keep a larger gap to the car in front and make sure you are fully insured.
I also told the employee that I've also purchased an extra (LIS) third party liability coverage which should work and cover the expenses.
Third party liability insurance covers (as the name suggests) third parties. Assuming that isn't invalidated it should cover the damage to the other car. If it is also invalidated you would be liable for the damages (material and medical) for the other party as well.