Not a problem with verifying anything I tell you. Checking on what you are told on the internet is always a good thing.
You have it correct, as I am sure Gigag04 will verify shortly. The trick to reading laws is to not read into them. The only things forbidden (in our legal system) are those that are explicitly specified in the law as forbidden.
So, when the law says a person but does not mention age, then the age of the person is irrelevant (whether 18, 20,21, or 65). In this case, the law says it is a crime to have a gun on or about your person if you are not in a car you own or under your control. The driver has the car under their control (generally, I am not sure of the way my daughter drives
). The weird part of this law is that the driver and the owner do not have to be the same person, so your sister driving your brother's car means both could have guns legally.