Dan Quayle was always much, much smarter than people gave him credit for. I share his prediction! : )
However, he is also easily manipulated. I woner if he got his take on the campaign from his former chief of staff, Bill Kristol. In his biography, Standing Firm, Quayle says that James Baker kept Kristol out of campaign meetings because he was intimidated by Kristol's intellect.
Now, I don't know about you, but I don't think Baker is intimidated by anyone short of Jesus Christ, and that smelled to me like a line that Kristol fed him which Quayle swallowed hook, line, and sinker. Since Kristol was well-known for leaking to the press, I think that the much more likely reason.
I still have the book in my library, and I am not mistaken about this statement. I reread the book when Quayle ran in 2000, and although I supported him, after I read the book (and certainly after 9/11) I wasn't so sorry he dropped out of the race.