Yes, but a graduate fellowship is just the extreme case of what is generally the case with the Ivy’s and similarly exclusive private universities: almost no one pays ‘rack rate’ except the rich whose kids get in on legacy or ‘leadership’ rather than grades.
My daughter went to Mount Holyoke, not an Ivy, but one of the ‘Seven Sisters’ from back in the day when the Ivy’s were men only, and there were comparably elite women’s colleges, and we paid about what a state university would have cost—a little more than it would have cost to send her to one here in Kansas, but less than U. Mass. Amherst would have cost us (and Massachusetts doesn’t have as huge an in-state/out-of-state differential as most states do).