Actually they do very often, on average 10-15 times per race. And a NASCAR is about 3 times as heavy as a average supercar. And they often travel at speeds approaching 210 MPH on a super speedway.
...that said, nothing about Driveclub remotely resembles a simulation. This game is visually stunning, but there's something about it that just doesn't feel right.
Exactly...nascar cars are very, very heavy...just comparing this to touches in forza 4 and especially forza 5 where you lose all sorts of control (thank you Turn 10 for finally making grass the frictionless surface it is at over 100 miles an hour)