The question isn't who can Congress naturalize. It can naturalize all the people in the world if it wants to. It has that power.
One question, for Cruz's case, is whether or not he is a citizen under the constitution. He is not. His citizenship depends on being naturalized.
Another question, for Cruz's case (as it was for Bellei), is whether or not he is a citizen. The answer to that is certainly yes, for Bellei (we have the record), and probably yes for Cruz (he is reported to have traveled on a US passport).
The naturalization process for those granted citizenship at birth is to present themselves to a competent tribunal, for example, a Consular Officer, and have the claim to US citizenship adjudicated. That process does not include an oath of allegiance, but it is a process. Only after the adjudicator has evidence that the statutory requirements have been met does the adjudicator issue a finding of citizenship.
I agree.
It is the way you have been applying the surrounding framework of what it means for Congress to "naturalize" is where there is solid ground for disagreement as to what it means for Congress to naturalize (an active verb there) a citizen, by statute.
Congress does not "naturalize" anyone who is otherwise born a citizen, even if clearly enough citizen under laws written of just who (just how and why) a person either is, or is not considered a citizen at time of birth.
There is no workable distinction between "born a citizen", and being a natural born citizen.