I think any autobiography needs to be dissected slightly and not taken at face value. This is true especially of an enigmatic personage like Waite.
Firstly, although he says outright that he had little to no hand in the Minors, they show obvious GD material as well as overall structure. There are things on them that Smith, despite her psychic gifts, couldn't have known. The cards themselves betray the fact that Waite was either lying or simply stretching the truth. Between the card meanings and general symbolism and description and rather obvious esoteric inserts like the Tree of Life or a Red Lion, the truth does come out, and isn't even that hard to find.
Secondly, there is the matter of the Courts. Like the Minors, they show clear Golden Dawn influence as well as hints to their proper places on the Tree of Life. Although the PKT describes them in one (wrong) order, the cards themselves once again have the information Waite sought in writing to conceal. The descriptions in Book T do fit the Courts, but in that book they are described in the correct order.
As to why Waite said what he said, I would assume it to be a combination of several factors. Ego would certainly play a large part, as much of his later career was re-forming the GD system into something that would better suit his more mystical tendencies. He would not want to be seen as a copy-cat. In addition, I got the feeling from other members' notes about him that he had somewhat of a chip on his shoulder, and was not the easiest man to get along with. Feeling perhaps snubbed, this would cause him even more to assert his own successes over others'.
Secondly, while he did eschew the magic of the Golden Dawn, he still utilized its initiatory system of grades, and in some of those grades much of the original GD material would still be of use, no matter what he said.
Still, something that's bugging me is this: In Crowley's review of the deck in the Equinox, he mentioned 777 as a published book. Although 777 is obscure (in order to use it, you have to know what it means), if it were, indeed, published already, it would mean many of the secrets were out already. Would Smith have consulted it, or known of its significance? Crowley also talks about how reticent Waite is in telling the truth, but his wording suggests Waite's secrecy is about things that aren't secrets anymore.