I believe despite disease the Aztecs did defeat the the Spaniards.
All three Spanish forces were comprehensively beaten in the battle of the causeways and left cowering in their camps assaulted day and night by Mexican forces.
It was a Texcocan Chief Ahuaxpitzactzin, brother of the Texcocan king, who bringing up a relief army to defend Cortez's defeated one came up with the plan to abandon the idea of assaulting the city and besiege it instead. It was the siege and starvation, not fighting which eventually lead to the downfall.
In many ways it was the Aztecs subjects not the Spanish who overthrew the empire, the Spanish just acted as the catalists.
The Aztec empire itself was born in an identical way when the Mexica themselves were a subject peoples in the hated Tepanec empire, who's capiatal was located not far from the Mexica's capital. The Mexica this time not the Spanish acted as catalist and banded together much the same cities as the Spanish were to array against them and lead them in a great seige and storming of the Tepanec capital. The Mexica then instead of liberating the subject people snatched the reigns of the empire.
All Meso-American history has a touch of deja vu and the Spanish affair was no exception.
Edited by Paul