What you're seeing on the INFO bar is the Hz and resolution of the *incoming* signal. Regardless of what signal comes in, the television will process and upconvert that signal to 1080p @ 240Hz.
Does that help explain?
I bought a Samsung LN52B750 TV yesterday. I'm excited to watch sports on the new TV because of the 240Hz refresh rate and 2ms response time. It's a large part of why I bought the TV. However, when I hooked up the digital cable box, I noticed that 1) the box is showing that it's 1080i (whereas the TV is 1080p) and 2) it's at 60Hz. Specifically, it says 1960x1080i @60Hz. Do I need to somehow change my television from 60Hz to 240Hz or how will i know that is converted and works at 240Hz?