That has been the general experience for most applicants. (Scholarships tend to be for some very unusual profiles - kind of like what is available on sale at Macy's - XXL sizes or shoes size 4 DD). So, unless you are an XXL size with a 4 DD shoe size, you are probably out of luck.
I believe HBS should have a gamut of named scholarships (just a hunch). Is there a resource available at school or can you ask the current students? I am sure eskimoroll, emont, shartperson, or a few others may know.
P.S. Good idea on scholarship "search" - never heard of it. It would be great to have a search engine for it at least...
Founder of GMAT Club
Just starting out with GMAT? Start here... | Want to know your GMAT Score? Try GMAT Score Estimator
Need GMAT Book Recommendations? Best GMAT Books
Co-author of the GMAT Club tests
Have a blog? Feature it on GMAT Club!
GMAT Club Premium Membership - big benefits and savings