That's just so much smoke and mirror treatment of laws pertaining to citizenship and naturalization. "It matters" you say? phhfft. It does not to the circumstances of McCain birth, and Cruz's also (though to lesser extent, Cruz having only one citizen parent at time of birth ---Cruz's own father becoming naturalized citizen only some time later).
Those individuals (McCain and Cruz) it is recognized within statutes were born as natural citizens.
That is different than "naturalized by statute" when the statutes are recognizing "nature" and natural birthright, albeit extended beyond physical borders of the United States.
The example in the link you had provided involved circumstance where neither of the individual in question parents were themselves born as citizens, and so would not apply to Soetero, to McCain, or Cruz either, for reason that U.S. laws do stipulate that person born of even only one citizen parent are born citizens of the United States.
From the pdf you had provided link for the 5th Circuit case;
v.
LORETTA LYNCH, U. S. ATTORNEY GENERAL
“Persons not born in the United States acquire citizenship by birth only as provided by Acts of Congress.”To interrupt here, "citizenship by birth only as provided by Acts of Congress" is not discussing one be naturalized by statute, but instead would be citizens at birth according to statute. In this instance, there were stipulations described by statute which were not met, hence the individual Jermaine Thomas be considered not citizen by birth.
At the time of Thomas’s birth, Congress extended birthright citizenship to children born abroad to one citizenAre you a "statutory birthright citizen"? I am. I was born in the United States. My mother and father and were born within the United States to citizen parents, as were their parents and grandparents and great-grandparents before them.However, it is undisputed that Thomas was not a statutory birthright citizen because his father did not meet the physical presence requirement of the statute in force at the time of Thomas’s birth.
The phrase 'citizen by statute' is not, and cannot be set against the phrase 'natural born citizen' as if there be some crucial difference there which results in not being "natural born citizen", for the former phrase (citizen by statute) does include the latter (natural born, ie., within the borders of the United States, to two citizen parents) even though there is recognition within statutes for there being natural birthright citizenship extended also in particular circumstances to those not born under the same conditions as was -- for example--- myself.