Einstein's thought experiment I'm referring to is this one: http://www.bartleby.com/173/9.html
briefly: train/embankment experiment is where lightning strikes at either ends of the running train (points A and B) and there's an observer inside the train (call him INSD), and outside the train (call him OTSD). if the observer OTSD sees the lightning strikes to be simultaneous, the observer INSD will see that one happens after the other. detailed explanation can be found in the link above.
anyways, so i get the reasoning. the speed of light is always constant, and from the observer INSD's frame of reference, the lightning strikes happened equi-distance from him, and since lightning on the front (B) reached him before the lightning on the back (A), then the one on the front (B) must have happened first... so what's simultaneous to OTSD is not simultaneous to INSD; i get it.
now, what i'm actually confused is;
assuming lightning stroked not the train, but the embankment outside, also at the same points A and B; and left a mark where it hit.
the observer INSD will still see the lightning strike from B first before A; but this time, observer sees where B actually hit the embankment; so can see the distance it actually traveled; which should be shorter..
that's the part i'm confused about; if the lightning striked on the embankment and left a mark there, can you still make the argument that both traveled equi-distance in INSD's frame of reference?
i know i'm missing something, but i struggled alone on this problem for a full day; and i don't have anyone personally to ask this question (not in school anymore); so please be nice and teach it to me like a little kid :)