Oh No, it is the point.
Ted Cruz's mother was an American. Therefore he is.
and invader's kids are not citizens by virtue of birth in a country not their own.
Tell that to the Hospitals in Texas and Hawaii giving out Citizenship papers to Birth Tourists from Mexico and China.
If you Have An American Parent, that makes you and American, whether you are born in Canada or Germany or anywhere else.
Not necessarily. Such citizenship is dependent on the provisions of the immigration and naturalization statute which is in force at the time of the birth. It's been that way throughout most all of our existence as a constitutional republic.
and invader's kids are not citizens by virtue of birth in a country not their own.
Tell that to the Hospitals in Texas and Hawaii giving out Citizenship papers to Birth Tourists from Mexico and China.
People here on tourist visas are here with permission, not invaders or legally analogous to invaders. (Does not mean that birth tourism is not a problem.)
All that proves is that people born in the US are viewed as US citizens. Most of them are also citizens of Mexico or China via the citizenship of the parents, by Mexican or Chinese statutes.
I think everybody agrees that Cruz is a citizen by operation of 8 USC 1401(g). What they don't agree on is whether or not his citizenship depends on that statute (although I think it does, as does the weight of precedent); and also if it does depend on a statute, whether or not that makes him naturalized.