The page says
"However, unlike the bent four in the corner, Japanese rules does not specify that any group whose eye shape that can be reduced to a twisted four in the corner is automatically dead. That is, the twisted four version of the "bent four in the corner is dead" rule does not apply."
I think this is a superfluous comment, because there is a good reason why such "twisted four" rule does not apply. As far as I can see, in those situations where a "twisted four in the corner" can be forced, better options are available, mostly downright kills.
The twisted four is only realistic as a direct result, not as a result from a forced reduction.
The fundamental difference between the twisted and the bent four is that the twisted one makes an eye in the corner.