I was banned from a business property for a incident that did not occur on their property, is this legal?

Question Details:

A chain store issued me a restriction from property notification due to an incident that did not happen on their property. I never signed this document. Can they legally stand behind the letter I never signed? The regional office also told me I was banned for life, which the letter does not state. The letter also has a spot for me to sign and they put n/a in it's place. I think they are just saying this because my husband still works for them, I know people that have stolen from them and were allowed back on the property.

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