"Oh No, He's Gonna Curse Me Out Again"

I had a person say this to me today after they called me back from a previous call where I was very upset by their customer service.

This company canceled my Tuesday appointment and then called at 2:30 this afternoon to cancel my Thursday morning appointment. They wanted to reschedule for NEXT wednesday morning. I was upset and I refused to settle the matter with an appointment a week out.

I was firm, but respectful. I NEVER raised my voice and never swore. I must admit I was quite surprised when the caller, who thought she had sent her techs to the wrong address due to my boss' name rather than mine being on the order, implied that I had treated her inappropraitely.

I am sitting here debating, is there a way to be firm, and not make the other person feel disrepected?