It was a lot more mutated than that, though it is essentially accurate. The ins and outs are rather interesting, however.
By 1800, the situation in Mexico can best be described as rotten, though interesting in its particulars:
http://www.fordham.edu/halsall/mod/1800humboldt-mexico.asp
Right after the rather vicious Mexican war of Independence (from Spain) in 1810-1821, everything started to change.
(starting at about the second paragraph here:)
http://www.tshaonline.org/handbook/online/articles/ugm01