There's no way thats image burn, but how are you supposed to prove that if they wont send another tech. I would complain bitterly.
There clearly is a problem with the TV (my guess would be the layers of the LCD are coming apart and dirt and/or condensation have got inside. I suppose it could be a problem with the backlight too, they are often cold cathodes, wrapped around the edge of the screen, although newer sets can use other forms of backlighting (IE LED etc) if its no longer an even light source I could possibly imagine that image.
If they just wont play ball, you could accidently toss a Wii remote at it, as your covered by accidental damage. While I wouldnt normally condone such behaviour, the warrenty/insurance trying to get out of what looks like a legitimate claim is out of order, so play them at their own game.
Its true that LCD's can gain a "memory effect" which causes them to get similar problems to a burned plasma... but a burn normally be a recogniseable shape/item, for example a channel logo/dogs etc, or a tape/banner like on the bottom of sky news.