To pass law about who must be naturalized, you must also decide who must not be. That is why the Constitution gives congress the authority to make any law necessary to implement the powers they have been granted under the Constitution.
The Congress shall have Power *** To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers, and all other Powers vested by the Constitution in the Government of the United States, or in any Department or Officer thereof.***
And how does that impact anything I've said?
I completely agree that congress can define who can be naturalized, and have said so.
The issue is that when one says that Cruz is a citizen and cites a congressional act, then they are citing laws respecting naturalization. They must be because this is the only sort of citizenship that congress has any authority over. And that means that they are implicitly claiming that he is a naturalized citizen, this contradicts the claim that he is eligible to be president (because that eligibility requires natural born citizenship, which is different than naturalization).