Can i be banned from this store? i didnt do anything.?

here is the story. my wife goes to this gas station one day and has a cashier be rude to her. she comes home and tells me about it.( im her husband) there are several people who work there and she could only describe the cashier and didn't know her name. after a little Q&A i was pretty sure i knew who it was. i went up to the store about a week later and spoke with the girl in question. she denied any wrongdoing, and said she didn't even remember anything happening. at that point i pulled out my cellphone and took a picture of her to show my wife so that we could be sure it was the right person. i went home and showed her and she said it was her. i could see that we were not going to get an apology or anything so i decided to just let it go and move on. a couple of weeks pes and i am at this same store getting gas and the very same cashier ask me if i ever figured out who was rude to my wife. i said that i was pretty sure it was her. i was willing to leave it alone but she just kept on denying it and saying that she never did anything like that. she then suggests that we file a complaint with the manager (her sister). so the next morning my wife goes to the store to get the managers info, and she will not speak with her or give her name or anything. we asked for corporate numbers and was told that the owner did not like to be bothered with complaints. we left frustrated and with no info. another week pes and im in the same store this morning to get water for my kids field trip, and the cashier says to me (not the same cashier) are you the guy that had the problem with "Dana" i said yes and she proceeded to to tell me that we were now banned from the store. she said they filed a police report and that i would be arrested if i came there again. can they do that? they don't even know my name. what crime have i committed?