There seems to be an assumption here that empathy leads to morality. Sometimes, at least, empathy leads to being jerked around by the stupid goals of others instead of pursuing your own stupid goals, and in this case it's not all that likely to lead to something fitting any plausible definition of "moral behavior".

Indeed; see http://lesswrong.com/lw/7xr/not_by_empathy_alone/ and in particular the should we section.