Ohio law on this has changed -- the CCW law has been amended multiple times since its adoption. Review the Ohio Attorney General's handbook on CCW laws. A close reading of this manual will reveal the AG's explanation regarding government parking lots versus private parking lots. If you receive any threats of criminal or civil action, please contact my office or another experienced Ohio attorney.
Ohio AG handbook link is attached below.
I am NOT an Ohio attorney, but many states allow for private employers to restrict the presence of weapons on privately owned property (just as they are restricted on government property)--so don't thumb your nose at the company just yet.
Additionally, a "loaded" weapon in the vehicle violates many states requirements.
You really should chat directly with an Ohio attorney to ensure you're within your rights re the company policy and OH law enforcement.
READ THIS BEFORE CALLING OR EMAILING ME: I am licensed to practice before the state and federal courts in Virginia. We have not established an attorney-client relationship unless we have a signed representation agreement and you have paid me. I am providing educational instruction only--not legal advice. You should speak with an attorney to whom you have provided all the facts, before you take steps that may impact your legal rights. I am not obligated to answer subsequent emails or phone calls unless you have hired me. I wish you the best of luck with your situation.
On private property, they can probably restrict you. Please consult an Ohio attorney to be sure. Either park off property, or don't bring the gun on property, for now. Keep in mind that it is possible for someone to break into the car and steal it. So, the less people know about it, the better.
The above is not intended to be legal advice, but may be used for general information. Please contact an attorney for specific help tailored to your needs. www.figgardenlaw.com