I thought that as well, but it even says 16:9 on the disc!
Anyway, I had a play around over the weekend. If I set the player to 4:3 output mode, the image is then presented as a mini-16:9 screen. As this gives large black bars top and bottom (as well as on the sides, but they're besides the point as the disc thinks it's 4:3 anyway) I believe this must be a widescreen image. I can then zoom it up to full-screen size. So I guess it's just a case of remembering to reconfigure the player to 4:3 before (and back again after) watching it. Strange, but there you go. Anyway, thanks for all your help. I can now watch it in peace without the screen bugging me!
Dan.