Yes, colleges can claim to “meet full need” however they define “need”. See this old thread for examples (not current, but you can get the idea): http://talk.collegeconfidential.com/financial-aid-scholarships/1675058-meet-full-need-schools-can-vary-significantly-in-their-net-prices.html
So it is best not to place too much importance on claims to “meet full need”. Instead, the college’s net price calculator is likely to give you a better idea of what its financial aid may be like for you.