Perhaps they do have such a record. But it doesn't seem any worse than many other states.
Ohio's made quite a bit of progress with respect to carry laws and such in the last several decades, though. They are a far cry from the way they used to be.
On the practical side of this issue...even if it's not posted precisely in accordance with the way the law says, it's not wise to consider this a loophole to be exploited. For one thing, he HAS discovered their policy, which means he can't honestly claim ignorance or to be uninformed about it now.
And even in the states where such postings don't carry the weight of law, it's generally not wise to deliberately ignore or flaunt them. Simply take your business elsewhere...and maybe tell them why you are doing so.