I guess I'm way too trusting, or I just don't sweat the little stuff. My neighbor is a PI and he can get any of your criminal records, social security numbers, license plates, etc. in a couple of minutes for about $100 per month. So if he can do it with little effort by just having minimal information on you, I'm sure some thief can do it also. This is just one of the prices we pay for the way information is gathered/shared/archived/lost/stolen, and the ease of access with current technology.
As for the dealer using the information for gain, which is fraud and most any dealer doing that is not going to be around for long.
The only reason they want the VIN is because of a change in the Mopar parts policies this last year. Most dealers are on a new system that any part ordered is not returnable, period. If the dealer orders it, it is his to keep forever. However, if he tracks the sale of a part and Chrysler determines it should be a stocked part, that part is guaranteed to be returnable if not sold. So if they are using StarParts, it VIN filters so the correct part is ordered. If you don't give them a VIN, the chance of ordering the wrong part is increased, and as long as you pay for that wrong part in advance I'm sure the dealer could care less.