Id say the word "have" doesnt have to be defined as "to be in posession of somebody or something", but could also be defined as "to be caring for somebody or something". So "I've got a sister" can be interpreted as "I am caring for my sister".

If we were to commit to this interpretation, we would have to for example weed out the instances of abuse. So mistreatment means it's not yours. If you cant take care of your car, it's not yours. Likewise, if somebody is hoarding cars, then they are not taking care of them so it's not theirs. They own the cars, but they dont have them because they dont care for them. "The billionaire doesnt have the yacht, tin owns it."

In a sentence like "Are you prepared to have the dog?" this would be the same as "Do you feel responsible enough to take care of the dog?"