Ya know, I've asked a few F-15 pilots and they haven't been able to give me a good answer.
I am assuming it's due to the F-15E's CFT's.
I've seen F-15C's with AMRAAM's both outboard (outboard when only carrying one AMRAAM and one Sidewinder...one on either side) and inboard, but never an F-15E with inboard AMRAAMS.
Who knows, I could be wrong, but it's just an observation I've made through the years.