No. Parking is leaving your possession somewhere and should apply to the registered owner. It is not illegal to own a car that someone else used to run a red light.
Surely the framing is "we the people allow you to operate this (otherwise illegal) dangerous vehicle on public roads, on the condition that by default you are responsible for whatever transgressions".
You absolutely can be, especially if you knew, or should have known, that the knife was likely to be used illegally.
While a bit more extreme than your example, there have been multiple cases where the parents of a school shooter have been held responsible because they provided access to a weapon when there were warning signs.
On the less extreme end of the spectrum, this is the same reason why you have to pretend that you are buying a "water pipe for tobacco" and not a bong if you don't want to get kicked out of the headshop (in places where that is still illegal).
3 year before the murder: You are probably fine, IANAL
10 minutes before the murder: Expect to get an accusation of accessory to murder, conspiracy to murder and a few additional tomes of the penal code. We all know you are innocent, but you should better find a good lawyer just in case instead of wasting your last free minutes arguing on the internet.
If someone used the car without permission, they are guilty of theft.
If they used the car with your permission, you should either be responsible for what they do with it, or be able to point to the person who was using it.
> If someone used the car without permission, they are guilty of theft.
Sure, but I still don't know who they are, so I can't give their name over for either investigating the theft or reassigning the speeding/red light/parking fine.
Except that requiring you to testify in order to absolve yourself of guilt violates your Fifth Amendment right not to testify in a trial against you. It is up to the government to prove you did something, not up to you to prove you didn’t.
You can not testify all you want, but you should still be on the hook for your vehicle getting tickets, just like you are on the hook for your vehicle accruing toll fees.
If your car was magically stolen and returned, and you have no idea that it happened, or who could have done this... Well, that's certainly an interesting legal argument that you could make to a judge. I doubt he'll believe you.
In the old days it certainly happened. Joyriding. Take someone's vehicle for a spin, put it back. Illegal but nowhere near as serious a penalty. Car security systems have gotten a lot better since then.