There is nothing on the link you provided that exaggerates his claim at all.
all the NT documents except two absolutely date from the 1st century.
First, the website you link to constitutes one man's opinion - and his opinion is definitely toward the anti-orthodox extreme. His use of evidence almost overwhelmingly cites Jesus Seminar associates and supporters - many of whom have never done professional work and who in total comprise less than one-tenth of one percent of NT scholars.
Second, even he admits that 22 of the 27 NT documents fall within a 1st century range of composition.
I'll also point out that the more work that is done, the earlier the dates seem to get - 30 years ago a significant minority of NT scholars dated Revelation to after 110 - now almost no one dates it later than 96.
Most of the arguments against the pastorals' 1st century provenance are based on the assumption that the Church had no hierarchy by the end of the 1st century - but research continues to confirm that the Church was well-organized from early on. Which makes good historic sense, since local synagogues indubitably had highly articulated structures of responsibility.