I have taken time to read over your initial question (with subsequent additions) as well as all of your responses.
You give an example of the following:
.......... "say you have a bunch of friends over you house ... one of them leaves, but hits another's park car causing minor damage (or under the 750 rule with no injuries) ... should that driver have to provide liablity insurance to the parked car's owner ...."
Answer to this is, you bet! ABSOLUTELY - just because this vehicle is parked on public or private property and damage is under the sum of $750 - that doesn't mean that the person who caused the damage (PARTY 1) is FREE AND CLEAR of having to show proof of insurance or pay - do you honestly believe that the owner of the damaged vehicle (PARTY 2) should be the one to pay? I think not! Party 2 has every right to seek out Party 1's insurance company to file a claim and to have Party 1 pay for damage. Should the damage of property be more than $750, then it is also reported to the DMV (SR-1 form).
You also state:
"For example, what if you were driving a tractor on a farm (or a truck for example) .... and say that the tractor hit another farm vehicle and/or a fence post ... would that 'farmer' have to provide liability insurance ... This might be an extreme example, but the LAW is the LAW right?'
Hitting a farm vehicle and/or a fence post - and possibly causing damage - my response is the same as above -
Here's an example for you:
Say that I personally smash into your vehicle while on private property and cause major damage to your vehicle - I drive away without showing you proof of my insurance....what are you going to do? Or, what if you asked me to show you proof of my insurance and I do not wish to show it to you and I just drive away??? Or what if the damage was under $750, but still your car is damaged and I drive away or I refuse to show you my proof of insurance.
What this basically states (should your theory be correct that it's not necessary to provide proof of insurance) - is that it's too bad for you and your vehicle - get your own vehicle repaired, pay for it yourself. In that case, I could be as reckless as I wish to on private property and smash up a whole bunch of vehicles and not show proof of my insurance. I can even knock down fences and anything else that crosses my path...!
The laws in the State of California apply regardless regarding liability insurance (showing proof upon request) whether it's on public or private property - it's considered a "road". Please refer to Vehicle Code Section 527 (a-e). DMV - V.C. SectionXXXXX/FONT>
If this information is not sufficient for you, then you may wish to do research at the law library.
I also provide you with the following links:
V.C. Section 17150 - Liability of Private Owners (responsibility to property)
I will state once again that, particularly in your case, when one is involved in an accident in the State of California - even if damage is less than $750, when asked, one must show proof of liability insurance - even if it is on private property.
Peace, Love & Happiness,
The Mystic Wave
Information provided herein is based on my 30 years experience as a legal secretary/paralegal in the State of California, with experience and knowledge in the State of Nevada. This information is not intended to substitute for informed professional legal advice from a practicing, licensed attorney.