Asian Buddhists are not atheists

In response to my twoposts below on atheism statistics, people in the comments and around the web (e.g., Facebook) have pointed out that Buddhism is necessarily/can be atheistic, and that Buddhism, is not/not necessarily a religion, and therefore that explains the statistics. Some of these people are lazy/stupid judging by the way the argument is delivered, but they are clearly grounded in a reality which is expressed in books and documentaries which introduce people to Buddhism. There is a small issue which confounds this analysis of the atheism statistics: most East Asians do not identify as Buddhist. This is mostly because most citizens of the People's Republic of China do not identify with Buddhism. That being said, Buddhism is clearly the dominant organized religion historically in many East Asian nations (though that has not been true in South Korea for the past generation). I reject the equivalence between the role of Catholicism in much of Europe and that of Buddhism in East Asia (the Church was a much more powerful, prestigious, and influential institution than the Buddhist sangha with only a few exceptional periods), but it can be argued that these are Buddhist cultures, just as they are Confucian societies. But there's a bigger issue with this objection: