Upon further poking around --
In iCal on MacOS, under the "View" menu, there is an option to show or to hide declined events. So I-- and I guess you and I think many people-- choose sensible to hide declined events. (*Why do I want to fill my calendar with things I am not doing?)
But iOS does not offer this option; and iOS seems to default to "show declined events". And for this reason, our iOS devices do not show the same content as our desktop devices. And this makes it feel, from a user point of view, like it is broken -- because functionally, it is broken.
(*Note that this seems to be a fairly old issue: in addition to the links above, there are also posts on this topic going back to users of mobileme -- and none of the threads have any comment from Apple, which is disappointing as attention to usability is generally the distinguishing feature of their products...)