True, but that's kind of a circular argument. Akin to guns are illegal because they're scary - guns are scary because they're illegal.
In this case it is not fear. Like I said before, if someone carrying a gun has no respect for the rights of the business owner, then I am going to err to caution that they probably have little respect for me, or anyone around them, as well.
I would call it simple prudence, not fear.
There are legitimate reasons a business may not want guns on the premises. Bars, are an extreme, but shining example of a business which is prudent in not allowing firearms inside.
Business owners also want to be absolved of any liability. If the insurance company is going to raise rates based on allowing guns to be carried, well,..there you go.
Fear is not the only motivator in making these decisions.