Grass holds moisture. It will accelerate the rusting from the extra wet environment. Park your car on gravel or concrete. I know personally from my own experience. Our muffler and pipes had to be replaced from our car being parked for a period of time in high grass.
If the grass is tall and wet and your car is metal....yes
No, I don't think parking your car in the grass is the cause of rust. I think it's leaving it out in the rain a lot, or something of that nature.