The theories don't correspond..they line up. MBTI doesn't measure Static/Dynamic, but the Pe Je crap causes MBTI's J/P to line up with Static/Dynamic.
If Introverted Rationals(JiPe) were deemed MBTI P(JiPe), and Introverted Irrationals(PiJe) were deemed MBTI J(PiJe) instead, then they would correspond.