Rock salt itself won't "eat away" at the paint. I come from 12 years auto body background and can tell you guys this:
Rust and corrosion begins at the factory. When you have bare metal and AIR, you get rust. This is due to the fact that air contains water.
Rock salt will damage your paint IF you rub it or go to a car wash. Slat contains silica, which is also found in sand. THAT will scratch you car. The best thing to do is to go to a SELF SERVICE car wash and pressure wash the car off, then soap it, then rinse it.
In all my years as an Auto body technician, I've never seen a car rot due to salt.

So to answer your question, just follow the above advice.