The Founding Fathers of the United States felt strongly enough about the right to own property and to be secure in your property, possessions and effects they made an Amendment that codifies exactly that. Life Liberty and Ownership of Property (The "Natural Rights") were the cornerstones of freedom, anyone who has read the papers and documents of history in that time period would know that too.
That being said, the right of a property owner on his/her own property is supreme. My right as the owner of a home, store, farm, wherever, means I have the right to do as I please. I am free to exclude anyone I want (However this has now been modified according to the Federally Protected Classes such as Race, Creed, Color, Sexual Orientation, Disability, etc).
If I, as the property owner, wish to post signs saying NO GUNS ALLOWED it is my right as the property owner to do so, and have a reasonable expectation that it will be obeyed.
There are not two seperate types of private ownership, "Private" and "Private, but with invitation". It is all PRIVATELY OWNED PROPERTY regardless of if there is a sign and a posted public open hours.
Once you enter my property my rules apply.
Your choice in this is simple. Enter my property and comply with the rules presented OR go elsewhere.
It is a very rare place of business that is so unique that it cannot have a competitor that allows CCW.
If enough people choose NOT to patronize that business because they do not agree with policies, the business will lose money, close down, etc.
Alternatively, if somewhere is so dangerous that you would absolutely not go there unarmed, I suggest you find somewhere else to go that is not so dangerous if you must use that service.
Should you choose not to comply with the rules I set forth for use of my property, you are not invited to come on my property.
If my rules are no guns allowed, guns are not allowed, regardless of the 2A. The Natural Rights of Life, Liberty, Ownership of Property are THE guiding force for the entire US Constitution.
For a good example, consider casinos. Gambling draws millions to casinos. But casino games are stacked in the favor of the house. If you can make the odds go in your favor, by counting cards (Which is legal) and start winning too much, the casinos will eject you and bar you from entry. You are doing nothing illegal. You are not even violating the gaming rules if yo ucan do it with no external assistance. But the casinos will throw you out anyway, because THEY are the ones who are supposed to win big, not the players!!
The US Constitution is also a set of rules for dealing with the US government. It does not apply to states or private individuals. You do not have a First Amendment right to free speech on this web site, for example. Why should some store guarantee your 2A rights?
HOWEVER:
It is *my* right as a gun owner with a valid CCW license to carry a gun anywhere that is not specifically forbidden by the CCW statutes. In Ohio those are .gov property, schools, etc. Ohio law also states that a private property owner may post in a conspicuous location a sign to that effect.
In OHIO the penalty for knowingly violating a posted sign is a trespass warrant, and that may only be cause for arrest if you are asked to leave the property and refuse.
With that in mind, there are many who recognize that a property may be posted, but knowing that they are not specifically barred by a possible felony charge, or that the signs are not "conspisuously posted" or that they feel that expressing one's 2A rights supercedes a silly sign, they will continue to carry well-concealed to protect themselves and are willing to face the consequences of that set of actions should they ever arise.
IN terms of consequences, how about speed limits. We all know speed limits are the law. How many of us drive in excess of posted limits? I personally drive 5-10 mph over habitually and sometimes much more than that. I am fully cognizant of the penalties should I be caught speeding and I am prepared to face those penalties. Therefore, I speed. Similarly, Criminal Protection Zone signs are just like Speed Limit signs.
After all, the law abiding gun owner is not the problem here, it's just the GFW's don't recognize a difference between a criminal with a gun and a CCW with a gun.
In Ohio prior to passing the CCW laws we had what was called "The Prudent Man Defense" which was not a CCW law, but rather a set of circumstances that were a defense to a Carrying A Concealed Weapon charge- if a prudent man would be having reason to go armed it could be presented that you were armed for that reason. Open carry in Ohio is actually legal, BTW.
So, to answer the OPs situation, people say "Concealed Means Concealed" because we are simultaneously satisfying our own desire to protect ourselves and our loved ones while also assuaging yet another GFW's irrational fear of guns by keeping it out of sight and not scaring the sheep.
How would a CONCEALED gun ever be a problem to anyone, anyway, as long as it stays concealed? Ohio does not have Texas-style brandishing laws if your CCW is printing out.
Does anyone think criminals are going to stop an armed robbery because as they enter the joint they see a no guns sign and realize they aren't allowed inside?
Please.
Concealed means concealed.
Carry on.