No. I didn't say the image was a fixed width (although it is, by definition), but that it is associated with various
<div>s, some of which have a fixed width and some of which have a percentage width. What's more, some have a max-width which means they are fixed width at that width or above, but variable below that width -- in standards compliant browsers.
As I said, the only solution I can see is to convert the widths of all the divs concerned to be fixed (px) widths. This will cure the problem you have (I think) but make horizontal scroll bars appear whenever the viewport is less than the number of pixels you specify as the width.
As to which is better, the answer is, it depends...
You have to make a judgment as to whether the removal of fluidity is preferable to the possible breakage of the layout in some circumstances. I guess it is, if you think those circumstances are going to arise frequently.