If another window overlays the window being imported (or grabbed) then you get an image of the overlapped window! Actually I have used that by attempting to grab a window positioned right but 'underneath' the desired import area
The only way of getting all of a web page in the way you describe is to start a virtual x server (VNC server) with a much much larger display. VNC can give you a smaller scrollable viewport into that virtual server. In this server you can start a much much larger web server window, to display more of the page, and the IM import can grab that larger image.
A script was submitted to the Im mail list some time ago that starts a virtual server, starts a web browser on that server and then uses Im to grab an image of the displayed page.
http://www.imagemagick.org/Usage/STORE/ ... t_webpages
I make no gurantees, or responsibility for this program. I just saved it for me (and others) to use.