I grew up in San Diego. Most definitely not Mexican food that people in Texas would recognize as Texmex but, according to many, would fit your description. The key difference between Texas and San Diego Mexican food is that Texas uses corn and San Diego avoids it except for corn tortillas.
To me at least, tex-mex is basically “Taco seasoning” and minimal traditional Spanish elements. I wouldn’t say corn is a requirement.
I grew up in San Diego. Most definitely not Mexican food that people in Texas would recognize as Texmex but, according to many, would fit your description. The key difference between Texas and San Diego Mexican food is that Texas uses corn and San Diego avoids it except for corn tortillas.