Yep!
Here's a clue. When Cortez conquered the Aztecs, there was NO SPANISH EMPIRE yet. There was barely even Spain, the country, much less, an Empire, at this point. I can't seem to understand why it is such a confusing matter for you to accept what is the reality, according to EVERY BOOK OF HISTORY ON THE SUBJECT, including the journal of the conquest itself written by Cortez's chronicler, an eye witness, which for the life of me, escapes my mind as to the title right now.
Check this page out if you want the most basic synopsis
http://emuseum.mnsu.edu/prehistory/latinamerica/topics/spanish_conquest.html