There’s also at least one that met full need based on FAFSA only (thus no NCP info) and that was Albright in PA. It served as a financial safety for my D for that reason. That was 2015 and I am not sure if it is still true.
There are some other schools that don’t promise to meet full need but might anyway that don’t require NCP info - Denison, Wooster (did have a NCP form that asked for very little info and NCP was never contacted).
Guaranteed full tuition/ride merit scholarships can also be financial safeties for kids with an iffy NCP situation. We’re crowdsourcing an update to that list now at http://talk.collegeconfidential.com/financial-aid-scholarships/2006094-2017-automatic-full-tuition-full-ride-scholarships.html