I think, too, that some schools might actually meet full demonstrated need without “advertising” that this is the case. That was our experience. Student did a lot of pre-research and hoped/expected aid at ~90% of need after we filed the css profile. After admission and a very easy FA appeal, they met 100% of our demonstrated need.
Although it’s a very limited sample, my takeaway is that if a school’s CDS shows they meet a great deal of need, and it’s a good fit for reasons other than financial, it’s well worth the application fee to find out what they’ll offer. This process is full of surprises… and they aren’t all bad.