The original comparison was with Singapore, so when I say "Asian", I mean developed east Asian countries: Singapore, Hong Kong, Taiwan, South Korea, Japan. I'll also include China in the mix.
I absolutely believe it's acceptable to generalize the above countries in this case, in the same way that I can generalize that most western education systems have less emphasis on passing exams and promote a higher emphasis on critical thinking. While it may be a stereotype, stereotypes are usually true to some extent, which is why they exist in the first place. It is true that the above countries do not have uniform education systems, and they are all different. However, they do follow a similar philosophy of passing exams above all else, and usually via a rote-learning mentality. FYI I'm from one of those countries, and I have an abundance of friends who have studied high school in those countries who can vouch for that. Likewise, my parents and relatives have all said similar things about the education system where they grew up - things like teachers only accepting one mathematical approach to a problem was wide spread, and is still wide spread to this day despite proposed educational reforms. Also, if I google Asian rote learning, there's an abundance of news articles about it, which goes to show that it's not simply a myth that can be brushed aside.
Learning names of elements, events in history, etc, doesn't qualify as rote learning. We all need to accept the basics before we can move onto my advanced things. The math example I gave above would be rote learning - just learning one method to do things and following that approach like a script. Another example was given to me a few weeks ago when I met up with some doctor friends of mine. They were at some medical competition, and the Chinese team was asked this question involving some organ, which my friends said they didn't quite understand. Unable to directly answer the question, they supposedly quoted 2-3 entire paragraphs, word for word, about the functionalities of the organ, but did not answer the question. My friends (as well as the judges) were amazed at how they were able to just regurgitate this information.
I never said rote learning prevents high marks. It works, but the downside is that it leaves little room critical thinking which is even more important. HK and SG also rank very highly on the PISA charts, but I have stacks of friends who have studied in HK and SG who can attest to their rote learning culture there. In fact, if you google those 2 countries, there's a lot of articles that seem to indicate those 2 countries are notorious when it comes to rote learning. The PISA scores that most of their population has a very good numerical ability and literacy. It doesn't have anything to do with how they learnt the material. It's significantly more likely that it's due to the cultural and societal importance of education in Asia when compared with the west. If you ask any of your Asian friend's parents, I'm almost certain a large majority of them will say that there's a much higher emphasis on education in Asia than in Australia. The entire PISA list can even be dominated by east Asia, but it doesn't change the fact that they have a much more rote-learning-oriented philosophy than the west.