Wrong. IANAL, but even I know that this would be dependent upon local laws, the judge's mood that day, and how connected the golfer is.
If anyone damages anything by accident, they are responsible for it unless a law states differently. If they damage something on purpose, that is criminal and totally different. I can guarantee there are not many (if any) localities in the US that state golfers are exempt from standard personal responsibility laws.
Yup, from that answer it's quite obvious that you're not a lawyer.
By and large, courts have adopted the idea of assumed risk for situations where a person lives by a golf course (refusing to hold golfers liable for wayward shots provided there was sufficient attempt to warn, e.g. the golfer yelling "fore"), so there's at least one immediate exception to your idea that, "If anyone damages anything by accident, they are responsible for it". Granted, operating a vehicle on a public road is different than voluntarily purchasing or occupying a house next to a golf course, but that still doesn't change the overall standard.
The standard is simply, "due care under the circumstances". Unless the OP can somehow prove that the golfer was negligent in the manner in which he hit the ball (e.g. hitting a driver for a 60-yard shot near the edge of the course, intentionally aiming for the road, etc.), there are precious few legal avenues available for recovery against the golfer himself.
However, there may be a path for recovery against the course itself, (though this is still iffy) on the grounds that the course failed to exercise due care by putting up netting. This is not to say that the course is responsible for the golfer's actions, but rather that the course is responsible for its own inaction. There are various methods used to determine just what sort of precautions constitute "due care" in this sort of scenario though and if the course can show, for example, that installing netting would cost $1,000,000 and only prevent $1,000 in expected damages, the course would probably not be held liable.
That said, for practical matters, the OP has a decent chance that a simple "nasty-gram" sent to the golf course will get his dent repair paid for. The course won't want to fight it and their insurance will cover it, so that's probably the way to go if he's set on recovery.
Disclaimer: I am a law student. I have not yet passed the bar and I am not currently licensed to practice in any state. This post is for informational purposes only and is
not an attempt to solicit business. Any information provided in this post should be confirmed by an attorney licensed to practice in your state.
ZV