Hey there—it is true that scholarships at Stanford are very rare. Let me give you an example—we had one girl this year who was offered a $40K scholarship to go to Wharton…and no money at Stanford. We have another guy who was offered a free ride at Wharton! And not a dime to go to Stanford. Scholarships at GSB are hard to come by—but that doesn’t mean that you shouldn’t apply! Who knows, maybe you will get lucky. Once you get beyond their first essay question (what matters most to you and why) you will find the application to be very straightforward, and the essays to be quite simple. So give it a shot! But your suspicions are correct—getting the scholarship will be veeeeeery difficult to accomplish…
although there is no scholarship, Stanford gives very generous fellowship (which you don't need to pay back). Usually 25%-35% of financial aid package, and you can borrow up to $170,000 with 5% interests rate to finance your study.
I personally don't know any M-7 school give out scholarship, although fellowship for sure..