Well, mexicans are mainly of Amerindian, Iberian or mixed descent. The Spanish presence of around 200 years means they can lay claim to some part of Spanish culture, much like many parts of the Caribbean. (Trinidad's Christmas music is based on Spanish guitar music 0_o

It depends on the person though. Someone may be proud to be called "Mexican" embracing the multiculturalism and individuality of their country, or they may feel like they are segregated from the rest of north America or feel the name is derogatory because of people's dislike of Mexicans. Those of Aztec/Mayan etc descent might feel offended if they are referred to as Spanish- they did kind of take over- and they may not embrace Spanish affiliation.
And someone dark-skinned from a Spanish speaking country like Trinidad or Cuba might be offended at being slows Mexican as it would be used as a blanket term for any 'racial mutt' (I refer to myself as a mutt...) that comes from a Spanish-ruled country.