Insurance company says i was 20% at fault?

It sounds like you ere following too close

You should be GRATEFUL the other insurance company is admitting to 80% responsibility. The general principal is that hitting another vehicle from behind is ALWAYS the fault of the driver that did the hitting.  This is because, if you had maintained the proper distance behind the vehicle in front of you, you would have had time to avoid the collision. Two seconds is obviously not enough. Any road safety course teaches you about speed, distance and stopping time.  You were clearly negligent here, and you are LUCKY that the other party is admitting to 80% responsibility. The rental company could be seeking 100% of the damage cost from you.

You will get nowhere in small claims court. Pay the $285.

If you paid for your rental car with your credit card, your credit card company should insure you to cover that amount.

Tell them that you were injured (whiplash counts as a injury) and should get something for pain and suffering.  Since you didn't get any medical treatment, they won't pay much, but they might agree that $500 is a fair amount of pain and suffering for your injuries.  Since they are saying that you are 20% at fault, they'd pay you only 80%, but that would still be $400, which is more than $285, so you could actually come out ahead.

I did the math and $356.25 is the minimum amount you need them to agree is the value of your pain and suffering so that the 80% will come out to at least $285 and you won't lose money.

Suing an insurance company for a debt you owe?  #$#$&#&%$& Seriously??????  No, you cannot sue them.  Well, you could try but you will need to hire a lawyer to do it and insurance companies have deep pockets.  You will be paying for that lawsuit for many years to come. You hit him.  How is it that you see yourself as not responsible?  If you were going at a speed where you could react in time and properly, you wouldn't have hit him.  Pay your bill and move on. 

You saw the car 2 seconds before... but the car did not appear out of nowhere, so you missed seeing it beforehand. 

- it doesn't matter if you don't feel like you were 20% at fault.  If you had insurance, they would determine you were 20% at fault too.  This is common based on the situation you describe.

What should you do?

HAVE A PARTY!!!! Thank goodness the damage as so minor, that you only owe $285.Wipelash is normally treated at urgent care or the ER. 

If you drive cars on a normal basis, you should get non owner insurance. 

Don't bother.   You WERE partially to blame.    You're supposed to drive in a way that you don't hit someone/something even if it's not supposed to be there.

Can you take WHAT to small claims?   You haven't been damaged.  You damaged someone else.

Next time don't decline the optional insurance.

You don't have an insurance company of your own? Did you purchase insurance through the rental car company? If so then they are your insurance company for this matter.

Sounds bogus to me, but insurance companies often play these kinds of games knowing that you'll probably not bother challenging them over less than $300. You could try to challenge it if you want to, but good luck fighting it for less than the cost of just paying it.

Also urgent care and emergency car facilities never closed for the pandemic, so if you had an injury you had every opportunity to seek medical care and get a proper diagnosis from a licensed doctor. If you claim "whiplash" at this point without having been to a doctor the insurance company will immediately flag your file as a potential scammer and they won't negotiate one penny with you unless you take them to court. There are far too many people who use the word "whiplash" loosely to try to milk car insurance claims for extra money. Never use that word with an insurance agent unless a licensed medical doctor formally diagnosed you with whiplash after a proper examination and x-rays.

Pay up the money you were following to closely

You were following too closely. When  a car hits another from behind, it's usually assumed that the driver in back is responsible. Be glad you're only being held responsible for 20%. And next time, allow enough distance to stop safely.