Even though the insurance may not say anything about it, the business owners are trying to avoid lawsuits by it.
Or the business owners are pandering to what they perceive to be the public preference. Realistically they may be fearing lawsuits...but posting a sign isn't going to stop any lawyer worth his salt.
Lets say I'm in Burger King having a burger (its almost lunch and I'm hungry) when Joe Jerkface decides to stick a pocket deuce-deuce in the cashiers face. Being a trigger happy militant crazy about to explode CC-er I draw my gun and scatter Joe's brains all over the walls.
Bully to you for the effective use of your CCW.
The next month Joe's estranged wife decides to sue BK for allowing guns in their joint, and decides to sue me for blowing his head off.
Anyone who chooses to carry..and subsequently use their concealed weapon, will face the specter of both criminal and/or civil liability. This is why you had best know the laws in your jurisdiction...bear in mind the lower burden of proof for civil liability.
Now, BK could have avoided getting sued if they had that "no guns" sign. It may not be an insurance policy, but that little sign will help them avoid having to pay out of their lawsuit insurance.
That sign, or the lack of it, isn't going to cut off or create liability for BK...however...in most jurisdictions BK will have a slew of formidable hurdles they could put up to insulate themselves from Joe Jerkface's claims. Including arguments turning on their legal duty to Joe Jerkface, any jurisdictional immunities like previously mentioned by Henry Bowman above, 3rd party arguments, etc.
This is exactly the reason my dad rejoiced after getting me off his insurance, because I'm a liability due to the sue-happy nature of people.
Ummm....you aren't a liability because other people might sue...you are a liability if you do things that give people a cause of action to sue you.