Schools that guarantee to meet full need (and are Need Blind) will always meet full need as the school determines that need for accepted students. What a school determines your need to be is not always the same as what the family thinks the need should be.
Also, some schools meet that need by including loans that a student must pay back. Make sure you research and find out which schools meet full need without loans and which include loans.
Be aware that many schools that market themselves as “Full Need” schools are also “Need Aware” when it comes to admittance. A Need Aware university might deny admittance to an academically qualified student because the school doesn’t wish to pay the amount of need the student would require. In some cases, this decision might be based on the school having already admitted the maximum number of FinAid needy students it can afford. For this reason, it makes sense to apply to Need Aware schools early so you can have your application reviewed before they shut off the aid.