Professional with 20 year career fired for going on a vacation with a female employee

I have been terminated for going on a vacation on days off with another female employee and asking her if I could share her hotel room with her on the last night. She agreed without hesitation, went and got a room, and gave me a key. We were in another state and had just completed a work project together and had a few days off before flying back to our respective offices in different states. The trip was completely consensual and we had a great time. I asked to share the room to save money. There was never anything romantic or sexual between us, we were just doing some traveling together. We each did our own thing on the last night and didn’t hang out together in the room. We left at 4:30 in the morning to go straight to the airport. We used the bathroom to change in, slept in separate beds, and I was not anywhere near her personal space. Apparently, this woman later decided to tell other women in the company about this and allegedly said that she felt too uncomfortable with me to say she did not want to share her room with me. All the other nights on the trip we slept separately. I was fired immediately, but not given any reason in writing or told what policy I broke. I cannot find a policy statement that addresses what I did. Is there anything I can do?