I’m no authority, but I have done a little reading, and it seems to me that we really have a couple things in play, as well as 3 or more styles of “Mexican” cooking.
First, Mexico is a big, diverse place, and it used to be even bigger. All of the southwestern US used to be part of Mexico- California, Arizona, New Mexico, Texas, Utah and part of Colorado. Parts of that were more integrated than others- San Antonio, for example has been a city since 1718, and El Paso has been around slightly longer (~1680) and Laredo slightly less (1755). On the Mexican side, most of the border cities are of similar age. So a Mexican presence in Texas has been there since the very beginning.
It’s not unreasonable to think that there might be 3 basic styles of Mexican cooking where Texas is concerned. First, there’s “Mexican” cooking- i.e. the stuff they have traditionally made in Mexico, specifically the parts adjacent to Texas. Then there’s Texas Mexican- this is the food made by Mexicans and Mexican Americans living in Texas, and is mostly an outgrowth of the Northern Mexican cuisine from nearby Mexico, with some local dishes and inventions. And finally there’s Tex-Mex, which is a fusion cuisine of Texas Mexican combined with Anglo ingredients and adjusted for Anglo tastes.
There aren’t clear lines between any of these though. Chili (con carne) is actually Texas Mexican, in that as best as anyone can tell, derives from a spicy stew that the original Canary Islander settlers of San Antonio brought with them in the eighteenth century, and has been refined/adapted over the centuries. So clearly not “Mexican”, in that it’s unknown in Mexico proper and even looked down on there, but it also predates Tex-Mex as well, being one of the dishes that started it. However, it came to prominence as a component of Tex-Mex. Fajitas are another Texas Mexican dish- Mexican and Mexican-American ranch hands in South Texas were given parts of the cattle that were slaughtered as part of their pay, and they’d grill it over wood coals with a simple marinade/rub, and eat it as tacos. So again, Texas-Mexican. But it was adapted and popularized as a Tex-Mex dish with a few modifications.
Some dishes are straight Mexican- stuff like mole poblano or pescado Veracruz are very Mexican, as are things like cochinita pibil.
And Tex-Mex is basically those Texas Mexican and a few straight Mexican dishes that are tweaked for American tastes and ingredients. Something like a cheese enchilada with chili gravy and orange cheese is straight Tex-Mex. A Mexican enchilada might be similar, but use slightly different ingredients such as a sauce made of dried chiles and a sprinkle of cotija cheese on top.
Some dishes overlap all three- things like carne guisada, tamales, guacamole, barbacoa, etc…
So authenticity is what you make it I figure. Nobody can really point at it and yell “Non-authentic!” because there’s so much overlap and culinary syncretism that’s gone on. Think about it this way… how absurd would it be for some French guy to piss all over Creole or Cajun cuisine because it’s not “authentic” French? Of course it’s not- it’s its own style. Just like Texas Mexican and Tex Mex are their own styles.
FWIW… I made Adan Medrano’s carne guisada last night for dinner from his “Truly Texas Mexican” cookbook- it’s fantastic! And it’s pretty much the exact same dish as you’ll get in any Mexican restaurant here in Texas as well.
Now as for whether or not that author’s family cooks were bad or not… I vote for yes. I mean, think of all the horror stories we’ve all heard about Americans cooking American food. But properly prepared versions of American classics are very tasty and good food. There’s no reason to believe that Mexican-Americans are immune to being poor cooks, or having a very limited repertoire. We’ve already seen that Texas Mexican and Tex-Mex are both delicious when done well.