The vehicle is not a extension of the home.
This is a hearsay that became a urban legend.
A judge once told me;
"If a vehicle is a extension of the home, why is it that it has to have a separate insurance policy once it leaves the property?"
"There is a difference between obtaining a warrant to search a home, and a officer searching a vehicle under "Probable Cause", which does not require a warrant."
"The law and the enforcement of carrying a loaded forearm in a vehicle differs from state to state, as it is a concern for public safety."
He went on jokingly;
"Why do you need a official documentation, such as DL, registration, proof of insurance always at hand in the vehicle and not so in your home?"
"Why is it legal to have sex, drink, and be naked in your home and not in your vehicle?"