You can stand on enemies that have platforms on them without activating the damage barrier right? Wouldnt standing on the platform (which is a part of the enemies body) be "contact?"
And if you remember the "lion" boss stage of mmx4.. you will remember that the boss in one of his specials actually charges and grabs X and then runs him into the wall without activating the damage barrier until he rams him into the wall.
I'm pretty sure the damage barrier.. being named a "damage" barrier.. is in direct relation to being activated by "damage" inducing attacks. And in all of the rockman series contact to non platform areas of enemies causes damage.. thus causing damage barrier activation.

And since throws are treated as single attacks and deal the damage as a single attack, the barrier would probably not be activated until the damage is dealt.
I will post some screenshots when i get the chance proving my point for the "lion" boss and the first boss of mmx1 and the platform theory so as to make the point more easily understandable.

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And another very interesting point to pose.. any direct contact to X would cause damage.. thus Cloud would not need to even attack him but just touch him and then run.