The net price calculators are probably the biggest improvement in college price transparency in recent years. Whatever colleges claim or do not claim, their net price calculators are likely to give more useful estimates than generalized averages for individual students and parents (unfortunately, it seems that many students and parents do not use them when looking for colleges).
Regarding NYU in comparison to other colleges, in http://www.collegedata.com/cs/search/college/college_search_tmpl.jhtml , it looks like NYU has the third highest student debt levels out of 53 colleges which are “most difficult” to gain admission to and for which student debt levels are listed (5 others do not have student debt levels listed). The two with higher student debt levels are Lehigh and CMU. Gettysburg, Brandeis, USC, Harvey Mudd, Juilliard, Notre Dame, and Emory are the next several after NYU. The lowest debt levels among the “most difficult” to gain admission to colleges were at Princeton, Webb, Williams, Harvard, Yale, Pomona, Wellesley, Haverford, Caltech, and Amherst.
*Yes, USC might be a target for your ire, as it claims to meet 100% of need but its net price calculator indicates that its definition of “need” is a relatively stingy one compared to others. Harvey Mudd and Notre Dame also claim to meet 100% of need. In contrast, Webb only claims to meet 80% of need.