You both seem to be saying the same thing - actively clicking on a like button gets counted as a real genuine user of Facebook. That seems reasonable (one is logged in, and clicks something sending data to FB)
Neither of you have said just having FB button appear on a 3rd party site counts - that would get what 3bn users :-)
Neither of you have said just having FB button appear on a 3rd party site counts - that would get what 3bn users :-)