The NAB, in none of its editions, makes that claim; neither does any other translation of the Bible. Please verify your facts before posting them.
The New Testament portion of the first edition of the New American Bible is translated primarily from the twenty-fifth edition, 1963, of the Nestle-Aland text. The Greek New Testament edited by Aland et al. for the United Bible Societies, 1966, was also used. Departures from these texts, however, are frequent.
The revised New Testament portion of the New American Bible is translated primarily from the third edition, 1975, of the United Bible Societies Greek text. The twenty-sixth edition, 1979, of the Nestle-Aland text was also consulted. This is just the reverse from the text of the first edition. Another change, much more significant, is that this revised edition of the New American Bible follows the United Bible Societies text much closer than the first edition followed the Nestle-Aland text.
None of these Greek texts are based primarily upon the oldest manuscripts available, but upon the data from a large number of manuscripts, some of which are much less old than others.