Let's say you've just been in a car accident, but it doesn't appear to be all that bad. The other driver offers to pay for the damage to your car or for your injuries, and it's a tempting offer. Perhaps you don't feel injured, or you don't see much vehicle damage. You don't think it will have to be repaired. Why not pocket a few hundred bucks and call it done? Besides, that would help the other driver out. Sure, he hit you, but he seems like a nice guy. He just doesn't want to involve his insurance company and watch his insurance rates go through the roof.
Don't do it!
There are a number of reasons why you should never make any kind of agreement at the scene of a car accident. There may be vehicle damage that isn't obvious, such as crumpling inside the bumper or underneath the car. And you may have injuries you don't know about yet. After an unexpected and stressful event like a car accident, your body produces hormones called endorphins. They mask pain. You may be hurt but not know it yet, or you may be hurt more seriously than you know because of the endorphins. No matter how you feel at the scene of your car accident, there's a good chance you will feel worse the next morning.
So give yourself a few days (at least) before you make any decisions about your accident. Maybe a better piece of advice is this: never make any agreement directly with the driver who caused your accident. Why? It's too risky. If it turns out that there is more damage to your car than you thought, or that you are more seriously injured than you thought at the scene, the other driver who wanted to just pay you may change his mind and decide that he can't afford to pay out-of-pocket for your losses. However, if too much time has passed, his insurance company might try to avoid paying because he didn't report the accident to them. All insurance policies require drivers to promptly report accidents to the insurance carrier.
The insurance company might not get away with avoiding the claim, but they could. Don't take the chance. Make no agreements directly with the other driver, at the scene or later.
The short answer is "maybe." There are a number of possible defenses against enforcement of an agreement made at the scene of your car accident. For example, if the other driver threatened you, the agreement would probably be void. Or, there may have been a mutual mistake of fact. If both you and other driver based your agreement on a certain fact -- for example, that there was no damage to your car that wasn't visible -- but it turns out that there is extensive damage that isn't visible from outside the car -- that mutual mistake of fact may void the agreement. And there are other defenses that might be available.
So, it's possible that you might be able to get out of an agreement that you made at the scene of your accident, but why take a chance? Make no agreements with the other driver.
Just as you shouldn't accept any informal settlement offer from another driver after a car accident, you shouldn't make such an offer yourself. Why? Too risky. In a worst case, an unscrupulous driver who accepted your money may simply deny the agreement and the payment. If that happens, you have no provable agreement -- and you have lost your money.
Besides, if you don't have a signed release from the other driver, your agreement at the scene may not be enforceable anyway. In fact, even if you could get a release signed at the scene, it still might not be valid because the person signing it at the accident scene may not be in a frame of mind to make important decisions and release valuable legal rights.
Propose no agreements at the scene. This is why you have car insurance. Report the accident to your insurance company and let them handle it.