All true.
“Records maintained by the federal government that pertain to Senator Cruz can be released under a Freedom of Information Act request.”
That assumes they still exist.
What records do you have from when you were 4 years old?
Certain key records, like a birth certificate are preserved.
But before the age of computers, many documents may have been destroyed long ago.
Government records are maintained. During the debate over Obama’s natural born citzenship, someone found the Certificate of Naturalization from 1843 for William Arthur, the father of President Chester A. Arthur.
The relevance of the document is that President Arthur was born with dual British-U.S. citizenship since his father did not naturalize as a U.S. Citizen until Chester was 14 years old.