You are probably looking at the source indicator. Sources of HDTV are either 60Hz or 24Hz. They correspond to the refresh/frame rates of TV and film, respectively. This nothing to do with how they are displayed on your screen. The refresh rate of you screen (600 Hz) is fixed and non-variable. It will refresh at 600 Hz no matter the source.
Why 600 Hz? That requires a little background: As noted above, the original frame rates for film and TV were 24 Hz and 60 Hz. Unfortunately for film lovers, when 24Hz films were shown in 60Hz on TV, they needed to display 24 independent frames divided into 60 frames per second, and the numbers just didn't work. So they had to use a process called "3:2 pulldown", which would display first 3 frames, then 2 frames for 60 frames a second, like this:
Frame 1 of film = Frames 1-2-3 of 60.
Frame 2 of film = Frames 4-5 of 60
Frame 3 of film = Frames 6-7-8 of 60
Frame 4 of film = Frames 8-9 of 60
Etc. This 3/2 cadence caused a judder in the playback of films on TV.
But now that we have higher refresh rates which are a multiple of both 60 and 24 (e.g. 120 Hz, 600 Hz) a 24Hz film can be displayed as the following (ex. 600Hz)
Frame 1 of film = Frames 1-24 of 600
Frame 2 of film = Frames 25-48 of 600
Frame 3 of film = Frames 49-72 of 600
Etc. Since each frame is displayed for exactly 24 frames on the TV, this eliminates the judder from the 3/2 cadence and smooths out the picture.
All this means nothing when viewing the refresh rate of the source, because the source is still (with some rare exceptions) either 60 Hz for HD video or 24 Hz for film.
