it's the wrap text. when you import an image into word the default wrap will be "in line with text" hence it will not overlap with anything on the page. when you just paste (ctrl+v) or use the paste ribbon the default wrap is most likely "in front of text".

you can change these settings as needed by selecting the object (image and/or text) then selecting the various wrap options (in line with text, square, top and bottom, etc.). Unfortunately I don't know where these can be found on 2003.