The way you said "and most folks seem to believe it" and ending with WTFO? implies that you believe it to be a fallacy. Am I understanding that correctly? In your second post, "I just know that you have a lot of the same protections in your vehicle that you would in your residence , but I'm sure there are some exclusions and I have never seen any actual legal language that specifies vehicles" I infer that you accept that as fact. I am not sure what side of the coin you are on here.Where did this originate ? I'm still hearing people say that it's " State law " and most folks seem to believe it . WTFO ?
Two things immediately come to mind. First, LA law makes no distinction in the so called "use of force" with regard to where said use of force occurs, be it at home, work, in a car, or in a brothel. As long as those locales fall between the Sabine River and the Pearl River, LA law applies. It is really a moot point, as the litmus test weighs circumstance, not geography, day of the week, lunar cycle or car vs home. None of those are mentioned, especially by name, with regard to defense of self. It is similar to LA's conspicuously absent "pre-meditation"; it is non existent in the criminal code for a reason. There is no such thing as pre-meditated anything in this state.
As far as the terminology, "an extension of your home" you will not find it (verbatim) in statutory law or criminal code. You will find it quoted in case law and appellate court decisions as a "plain english" explanation of decision. It is intended to easily explain a judicial concept to lay people. It is easy to understand, as opposed to legal jargon.
Recently, I was explaining a mechanical procedure to a novice / entry level class. The process involved physically shifting a large gearbox, known as a transfer case, from one mode to another without damaging it. I directed the students to complete a series of checks and double checks to ensure all internal rotation has stopped, then BRISKLY shift the up/down selector from one operating position to the other WITHOUT stopping in middle position. A bystander/co-worker with a less than stellar reputation interrupted the training by blurting out, in front of everyone, "You didn't tell them to stop in the middle neutral position, the factory representative TOLD ME to stop the selector in the middle neutral position!" I politely explained that I would address the discrepancy privately after the training, but he insisted that I explain immediately and in front of everyone. I accommodated him by saying that when the factory reps think that the end user is a dipshit, incapable of checking and double checking instruments to ensure internal rotation has stopped, they just tell them to stop the selector in the middle neutral position to add a few seconds to the process, ensuring that the dipshit doesn't damage the machine if he read instruments wrongly. In other words, there is no mechanical reason for stopping in neutral, it just adds extra time to the process to safeguard against damage by inept operators who might shift while internals are still spinning. I went on to explain any time the factory rep suspects the end user is a dipshit, they explain the process this way. The rude coworker turned red and stormed off while the class laughed at him, realizing there was a reason I wanted to explain privately. This is much like when a woman goes into labor, and they send the hysterical guy in the group to "go boil water!" The water has no purpose, but it gets rid of the asshat in the room for 15 minutes; by the time he gets back the crisis is over with.
I liken these simple expressions to the above examples, a simple phrase or cliche uttered to be understood by all, regardless of literacy, educational level, or legal knowledge. If you look at an anatomical chart, there is no "Adam's Apple," but there surely is a larynx. They are one in the same; one is a layman's term, the other medical terminology. The "extension of home" is not a legal term, but a legal concept easy for all to understand.