From the article:
"Today, the most striking institutional feature of Japanese rail is that it is privately owned by a throng of competing companies." ...
"Core rail operations are profitable for every Japanese private railway company, but they usually only account for a plurality or a small majority of revenue. The rest is contributed by their portfolio of side businesses."
It's like a textbook good application of capitalism that unsurprisingly the US can't seem to get right.
[1] https://flippa.com/blog/pe-funds/japan-private-equity-firms/
I fail to see how the topic of this comment thread (namely "why Japan has such good railways") sheds any light on the US PE industry or vice versa. Maybe you can explain the link. (If you can't then your cheap dig is also off-topic.)
(And I fail to see how antitrust law in particular might constrain a PE firm in any way.)
Additionally, the stations are generally owned by private companies—including the the development rights at the station. This means that the Japanese private rail companies capture a portion of the value created by the rail service, which otherwise would be an externality. So the companies have an incentive, as landowners, for rail ridership to stay high.