It's not a myth - at least, it might not be a problem on a high end Kuro, but I assure you on my entry level Samsung panel (bought in 2008) I get traces of game score counters, or that bloody CBeebies channel logo, showing up even the next day.
The worry of permanent burn was enough to make me turn the contrast right down on the Wii input.
The manual for this panel has screen burn warnings on the front page, and a statement to say that screen burn is not covered in the warranty. The menu also has several options for avoiding or rectifying screen burn (a whitewash, a b/w scrolling pattern, options to pixel shift a PC display at periodic intervals, and for setting the brightness of the "windowbox" bars when displaying 4:3 material).
Conversely, my Hitachi LCD panel has none of these options. It mentions image retention briefly in the manual, and says it can easily be rectified by turning the display off.