since I haven't lived in CA for twenty years. California distinguishes between titles for completely new cars, and titles for rebuilds -- if the car's been salvaged and rebuilt, it will show on the title. I don't remember what the phraseology is like.

And yes, pulling the mats out of the flooring and trunk will reveal any ripples or bends in the floor panels and the places where the floor joins the wheel wells. Also see if the seams are all lying flat -- if the car's been seriously bent, there will be places where the seams don't quite completely meet, possibly including broken spot welds (though that's unlikely). Looking underneath is still better, though.