Can an employer discipline you if there is no formal complaint against you?

[Gamaliel]

I am a male and my co-worker is a female. One day we were working together and I offered to buy her lunch. We were standing in line at Subway trying to choose a sub when I put my arm around her and said " so what are you going to have" she chose a sub and I paid for it. we then sat down and ate while we chatted. We continued to work and later exchanged phone numbers. A third party felt that I was harassing her and reported the incident. At no time did my coworker appear or ever tell me she felt uncomfortable. They(my employer) questioned her and she confirmed that at no time did she tell me that my actions were unwelcome or made her feel uncomfortable. My coworker was asked to file a formal complaint against me and she refused. I was later questioned about the incident and told them the same thing, at no time was I told that I was making anyone feel uncomfortable. It appeared that my employer was trying to force a complaint against me from my coworker. I feel my employer is guilty of attempting to create a hostile work enviornment. Am I right?