That message means that you used somebody else’s API key to activate the plugin.
Who owns the API key you used when you first activated the plugin? Get that person to add you to the access list. The form for that is on the stats reports page.
The stats are computed by wordpress.com, so that’s where the reports are generated. You need an API key to activate the plugin, therefore you must have a WP.com account.
Your partner can add you to the blog’s stats access list using the form on the stats reports page.
Try print_r($cat) to see what’s there. I’m not sure what version you’re using, but I work on the latest stuff and I know we have $cat->category_count in the 2.1 alpha.