The page that it's working on, I only see the "Like" button, not the share. Unfortunately, from more investigation, Facebook basically recommends not using the Share button anymore (it's being phased out), but instead using the Like.
They also recommend adding some extra meta tags to the page which can set a custom title, description, and image to display when a user 'Likes" a page. We'll be adding options for these tags in an upcoming version. With the Like button, as it currently is, you're users can add a comment about the page. If they do, it will show up like a Share in their wall. If they don't add a comment, it will add a one-liner to their wall that "I like xxx".
We're still working on the compatibility issue, but for now, hopefully the above information helps.