What does the "clause" in your policy say? I've never seen a policy that contains language to this effect.

Typically, this is not addressed specifically within a policy. If you own the car outright and want to keep it, you can keep it, and your insurer reduces the settlement amount by the projected salvage value amount. If you do not own the car outright, it is up to the leinholder whether or not you can keep the car, since they are actually the titled owner. They usually don't allow it. Not always, but usually.