Q. So, technically, if a student has only earned income and scholarships, it doesn't matter how much they earned (can be even 10% of their support), and as long as the rest in scholarships, they can claim the credit?
A. It would be unusual, but yes.
Don't forget non cash support. The most common item: the support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.
From Pub 926 (page4):
"Services not of a household nature, such as services performed as a private secretary, tutor, or librarian,
even though performed in your home, aren't considered household work".
https://www.irs.gov/pub/irs-pdf/p926.pdf
