And even then, it has no actual legal effect if you do, because at death your body becomes the property of your next of kin. It's just another part of the estate. They absolutely can override your wishes, and the most you can do is put a clause in your will that says "if my organs are not offered for donation, Andrew gets $0.10 (ten cents) inheritance; if they are, he receives 100%".
Which is weird, because I've never spoken with anybody who hasn't opted in. I think there's a legal disconnect somewhere, where the simple opt-in at the DMV doesn't end up counting as a 'real' opt-in.
This is such a ludicrous theory that is sadly repeated often. It is extremely unlikely that your set of organs will be compatible with someone they know who needs organs. Even then, a nurse or allied health professional is much more likely to make a medical error which kills you. You'd be surprised at how thin the line between life and death is, especially for people on death's door.