I seem to remember some earlier thread saying that US Irregulars do not go to casualties even though a bullet under 3.3.3 Attack says...
Your assessment that follows is correct: Irregulars DO go to the Casualties box. The rule has not changed.
Where the confusion arose in that other thread was whether or not Irregulars go from the Casualties Box to Out of Play. (The answer being "not during normal play, but events override the rules per 5.1.1").