I can hardly imagine a substantial legal discussion between a common law, continental law and, say, shariat law scholars...
So maybe the diversity of thought is not really a good idea for law doctorate...

Anyways, I know HBS was offering fellowship for any doctoral student regardless of origin.
So I somehow extrapolated it should be the same for HLS...

Isn't it?
Which university did you apply?
Which branch? Trademark and patent?