If I understand this correctly, the bursaries are not needs-blind or means-blind or whatever at Eton. The offers for a place are (or they are aiming for that, anyway).
The idea, on paper, is that they offer places to whoever best fulfils their entrance criteria, with no regards to any financial needs.
Then they make sure that everyone who was offered a place can actually take it up, so - dependent on each family's financial circumstances, one child would get a 100% bursary, another a 15% bursary, a third would get nothing at all.
The difference being that in most schools, you apply for a place (and a bursary at the same time). You get offered the place after e.g entrance exam. Then your bursary application gets assessed and you may or may not be awarded a (sufficient) bursary, so you end up having to say no to the offered place. If the school really likes your child they might be a bit more likely to offer you a sufficient bursary, but they will certainly not be offering to every applicant who passed the entrance exam and needs financial help. Out of all the children who passed the exam and applied for a bursary, some will be awareded a bursary, some won't. How many are awarded a bursary, will depend on how many full-fee-paying children are in the intake that year.
Whereas at Eton, if you pass the exam and are offered a place, and need a bursary, you (supposedly) are certain to get that bursary. They will still check your finances, so you can't get a bursary just by claiming you need one whilst leading an expensive life-style. But finances won't stop your boy from going to Eton if he passes the entrance exam and is offered a place (and that offer will have been made 'needs-blind' meaning they don't check to offer places only to those who can afford the school).
So, every boy who passes the exam and is offered a place, should be able to take that place up.
However for now that is their intention, and hope for the future - they aren't quite there yet. This can cost the school a lot of money. Eton is rich enough that they can go a long way in this direction, but if 70% of the children passing the exam need substantial bursaries to pay the fees, and only 30% will be fully fee paying, then even Eton won't be able to offer 'needs-blind'. They need enough 'paying customers' in order to be able to afford to let the rest attend 'for free'.
As long as a large majority of applicants for Eton is capable of paying full fees, they can offer to anyone who passes the exams without checking finances first, and then pay bursaries to that minority of applicants who can't pay full fees. At the moment it is about one in five that receives financial support, which is a lot, but still means that 4 in 5 pay full fees.
If lots of less wealthy families were to apply, they could not offer 'needs-blindly' to everyone who passes the exams, or they would end up with 10% of rich students essentially cross-subsidising the 90% who also passed the exams but can't afford the fees. That would deplete their reserves very quickly, and the wealthy families would no longer go there anyway.
So they can only offer places 'needs-blindly' as long as the large majority of applicants (who pass the exams) can actually afford to pay all or at least most of the fees.