It's either Mexico and Texas, or Méjico and Tejas. Someone might mix across languages, but that does not mean that there is actually a formal exception to the rule.
Not at all. In Mexico, it's written México and pronounced Méjico. So that is definitely an exception to the pronunciation of x as a ks sound.
The spelling rule you imply is not correct either: the same Spanish speakers who write Texas for the state, write Tejano for the Latin music originating there--both of those spellings being the most widespread in both Texas and Mexico.
So I dug this up a bit, because I'm accustomed to the form "Méjico" in Spain.
You are right that México is written with an X but pronounced with a jota. However it has a special status of topónimo (place name), which sometimes don't have a translation (thank god).
E.g. "Washington" is not pronounced with a sharp S, it's just pronounced as in the original language. Or Wyoming is pronounced as "uaióming", not "bioming". Which is exactly what happens with México, in old spanish the X was pronounced as jota.
