In the U.S., people tend to be keenly aware of school differences, because public schools have a lot of local autonomy and are typically locally funded. In Japan, because the curriculum and many other education-related matters are determined by the Ministry of Education, there is a large degree of apparent nationwide uniformity, especially between grades one and nine. For example, in every elementary and junior-high-school classroom I have been into in Japan, and in almost all that I’ve seen in photographs, all of the desks face the front of the room and the outside windows are on the students’ left-hand side [1]. There doesn’t seem to be any similar uniformity at least in California [2], where I went to elementary school more than fifty years ago.
This apparent uniformity can give people who have experienced Japanese schools only as students the impression that whatever they happened to experience in school—a lot of bullying, say, or none at all—must be typical of the entire country.
Of course, people in other countries might overgeneralize their individual educational experiences, too.
[1] Google image search for 小学校 教室 [elementary-school classroom]
https://www.google.co.jp/search?q=%E5%B0%8F%E5%AD%A6%E6%A0%A...
[2] Google image search for elementary-school classroom California
https://www.google.co.jp/search?q=elementary-school+classroo...
My impression is that, overall, the bullying is probably not significantly worse than in other countries, but that perhaps more media attention is focused on the issue than elsewhere. There was a major moral panic in the mid-1980s about school bullying, and the media continue to report regularly on statistical trends and extreme incidents.
Anecdotally, there seems to be a lot of variation among schools. More than one public school teacher has confided to me about how different the kids are in different neighborhoods. Japan may seem homogeneous, but there’s a lot of local variation by social class. In the tougher schools, there can be fighting, stealing, and bullying, while in other schools that might be practically unknown. Private schools can be very different from public, too, and there are a lot of single-gender schools, which have their own dynamics. Certain aspects of Japanese culture, such as age-based hierarchies, may be stronger or weaker or play out differently in different types of schools as well.