Just because a show is the best-reviewed doesn't mean it wins. The "quality" of a show can only go so far in a voter's decision. It's mostly politics.
No one ever promised "proof" or hard facts that the Q campaign 'swayed' votes from another show to Q. It's just a given that it had influence. Can you provide proof that it didn't?
I mean, let's face it. If QUALITY was the most influential factor in giving out the Tony, then the history of shows that won would be quite different:
GREY GARDENS over SPRING AWAKENING
THE COLOR PURPLE (or DROWSY) over JERSEY BOYS
THR LIGHT IN THE PIAZZA (or ANY of the other shows) over SPAMALOT
CAROLINE OR CHANGE over AVENUE Q
URINETOWN over THOROUGHLY MODERN MILLIE
THE WILD PARTY over CONTACT
PARADE over FOSSE
RAGTIME or SIDE SHOW over THE LION KING
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle