Just thought I’d chime in. The problem for me was similar to what oreixa described.
Basically anywhere in the function stats_get_blog, the array will have a bunch of get_option() calls. Wrap those in utf_encode() and it can solve the parse error.
I’m guessing that the plugin is sending an XML request in UTF8 but if your blog isn’t set to UTF8 (like mine wasn’t – I’m ISO8559-1, I believe), then it would end up as crap characters and would essentially look like a parse error.
Doing this will force everything to be UTF8 and everything should just work.