If this were true in general, there wouldn't be any liability insurances - which covers exactly these cases.
However, there are also situations where the statement would apply. E.g., over here in germany, if an employee accidentally* causes damage to their employer (say, break their work laptop) the employee is not liable (it's considered a normal business risk of employers).
*or even negligently, as long as it isn't gross negligence
If you weren’t negligent then sure you didn’t do anything wrong
There is a concept of strict liability, where someone can be held liable even if they were not at fault. The idea is that some things are inherently dangerous but legal.
Examples (here in germany) would e.g. be
A car is considered to pose a certain inherent risk. There are certain requirements to minimize this (safetying, driver's licence, forbidding drunk driving ...), and the keeper of the car must have a liability insurance (to mitigate the financial risk for others).
However, §7 StVG does not require the keeper of the car to be at fault or negligent:
(1) If, during the operation of a motor vehicle, a person suffers death, the body or health of a person is injured or an item of property is damaged, the vehicle holder is liable to make compensation to the injured person for the resulting damage.
Thus, e.g. if there is a bicycle - car accident, damage (and liability) the car will be assigned at least partial liability unless the bicyclist is proven to have been in gross violation of traffic regulations. (Below that, the bicyclist is liable for partial damage to the extent they are proven to have violated traffic regulations, but every uncertainty i.e. the mere possibility of the driver having been negligent is assigned to the car's inherent danger. Even a properly parked, switched off and locked car can lead to liability.)
Similarly, §833 BGB for pets:
If a human being is killed by an animal or if the body or the health of a human being is injured by an animal or a thing is damaged by an animal, then the person who keeps the animal is liable to compensate the injured person for the damage arising from this. [... exception: for non-pet domestic animals as long as the keeper was not negligent...]
Example: I have a watch dog. The grounds are fenced, and the door closed. The door post has a sign on eye level saying that there is a dog running freely inside, and tells people to ring. We had hired a builder, who came half an hour earlier than they had said. They opened the door by putting their hand through the bars right beside the sign, and drove in. The dog was still out and got excited and jumped at the car, and some stone at his paw scratched the paint. While this was solved amicably (when we showed the sign to the builder he said he doesn't understand how he could have overseen the sign; and the scratch turned out to be shallow enough to be repaired by polishing), my animal liability insurance told me that regardless of any trespassing, as keeper of the dog I have full liability for any damage he causes.