You can get that level of damage immediately in arcade mode. I posted this on another forum...
If you want to see that same level of damage, take the Ford WRC car in arcade mode, wreck it for about 15-20 minutes (or less if you choose one of the Ovals and drive into oncoming traffic) and you'll get that level of damage. Mechanical damage-wise, you'll start to notice the car pull to the side once one of the doors opens up. When both doors become loose, you won't be able to rev very high. Once one door falls off, you'll get a trophy and it will start pulling to the side that still has a door attached. Once both doors fall off, the mechanical damage seems to go away (or at least you're able to rev higher again).
I seriously doubt damage "unlocks" at certain levels (or at least until a patch is released). I'm also thinking this level of damage might only be possible on WRC cars but I haven't tested it yet on many other cars, so that's pure speculation. The NASCAR stock car I tried wrecking ended up looking like a car out of Daytona USA (seriously, the trunk bounces around when you're on the grass, otherwise the car just looks deformed). The BMW M3 I tested just looks odd after a few high speed wrecks.