That is what DMM wiki claims, yes. How true that is is... questionable. But certainly a strong possibility, since I don't really trust the DMM devs on actually programming shit right.(Possibly) true, but I very much doubt that it's actually harmful. I mean, unless you reach 100% combo rate, you'll gain more double attacks than what you'll lose triple attacks. As such, Rush should still always be an upgrade over non-Rush. Unless your entire team is Brahma with a "guaranteed combo" skill. I don't agree with Laventale's statement at all. Shingen's +15% Double +10% Triple should be nowhere near enough to put your team into a state where using Rush would be a downgrade. Even for Awakened Hime, there's still 60% non-combo rate space there.
Just notice that Rush is not a replacement for Assault. Assault is still by far the strongest skill you can get (so far), and every single weapon in your Grid should have it. Pride is Assault, so that's fine too.
And on a note, I haven't properly mathed out either statement since I just don't care enough anymore.