A parking lot is a parking lot for a private business. No restriction on keeping a firearm locked in the car.
However, the termination letter in the file will read, "During the employee's probationary period. it was determined that the employee is not a good fit for the position for which they were hired. There are no other current openings for which the employee is qualified to fill. The employee's last day is X. They will be paid through the end of the day. COBRA paperwork will be mailed to the last address on file." Or something along those lines.
Some people in the HR industry don't like to be told they are wrong. I sent a copy of the state law adjustment regarding employer liability as it relates to allowing or prohibiting firearms on the property to a HR consultant for a local Payroll company. This was after I told her in my office she was wrong. I did say it in a nice way. I got no response from her.
If you want to politely push the issue then gather your facts with plenty of references. Do not go in and say well so and so on this internet forum said. . . . If you don't want to push the issue. Then keep quite about storing a firearm in your car.
They guy I was talking with isn't HR, and I have no desire to try to send them any info or get them to change any policies either. Concealed is concealed as far as I'm concerned.
No win situation here. You could sue them if you were fired, but would your damages be enough to cover everything? And then the stigma that hey, here's the guy that likes to sue his employer. Not a good note on the old resume. What does your company do or produce?
Worth noting that the Oklahoma courts have held that it is a bona fide crime -- not just a civil matter that you can sue over, but an arrestable, cuffs-on-the-wrists misdemeanor -- for a company officer to attempt to enforce a ban on lawfully owned guns in their parking lot.
Post the email address of the HR/legal dept and a few of us can inform them of this law, for their information. You might not be involved in a way that connects this to you.