YES, I have a Hitachi 57F500 and it was coming on by itself at night. The problem was coming from the remote(s) when the house cooled off at night. Although, I'm not sure which one because I messed with the TV remote and Dish remote and the problem went away.
I am using one of the older Dish network black with blue button remotes. The AUX button is setup to turn on the TV. It seemed very sensitive to the lightest touch. The Aux button had some goo in it that was keeping it almost pressed most of the time. I took it apart and cleaned the goo out.
Also, I noticed the Hitachi remote power button was very sensitive. If the button was barely touched, the TV would turn on or off. I cleaned it and messed with the rubber button a bit until it was harder to operate.
The problem went away, but since I didn't do one at a time, I never knew which one fixed it. Now that you are having the same problem, I am betting on the Hitachi remote.