Another possible workaround is to select the image in Illustrator, hide every other image in your document that you do not wish to copy over, fit artboard to artwork bounds (Object>Artboard>etc.), save as SVG and grab the code particular to your preceding isolation work from the SVG dialogue, past the code into Muse's "Insert HTML" dialogue, then scale the resultant shape based on the axis that matches the particularities of its bounding box (in my experience, either the width or height of the resulting image's bounding box did not fit to the edge of the graphic, so I linked width and height and adjusted the value of whichever axis fit to the edge of the graphic.
I imagine straight copying and pasting of the image itself into the Muse HTML dialogue adds additional information about the placement of the shape within the context of the artboard.