I agree, except it isn't about the right to have a gun in your car; it's about whether the guy that owns the parking lot has a right to say who's allowed to park in it.
Inside a business building is one thing, but in the car means that there are two property rights to balance. Does the owner of a parking lot have a right to know what is inside each car? I don't think so. Sure, they can deny access to anyone they choose, but they don't have an automatic right to know or even ask what is in the car.
I can, for example, allow or not allow someone to park in my driveway but that doesn't mean I can search their car, or even have a right to ask them what's in it. If I can't ask them what's in it then I've also got no business demanding that it contains no guns.
There are competing property rights here. I would submit that contents of cars are out of bounds.
If an employer can tell you what you can have in your car then he can wreak havoc with your life, what if he doesn't like baby seats, how do you get your kids to and from school or daycare? Can she ban the bible? or leather seats?, can they ban tire gauges, how about spare tires?
Close, no cigar:
what it's about is whether or not your employer, the "guy who owns the parking lot," has the right to deprive you of your Constitutional rights on the way to and from work
Now if you hate guns, fears guns, or think guns are somehow inherently evil, just say so, but don't try to confuse a rational discussion.