Not to put too fine a point on this, but American citizenship is not “automatic”. For example, had no one applied for US citizenship for Cruz, he would have zero proof that he was even eligible for such. Waving his mothers birth certificate at a border crossing or under the nose of an offical while trying to get a US passport would simply not work.
His mother would have had to do the following. There are links withing the PDF to the other actions also required to attain that not-automatic US citizenship.
http://photos.state.gov/libraries/canada/303578/montreal/crba_eng.pdf
I think it is a very fair question to ask to see Cruzs CRBA. He has released his Canadian birth certificate, his mothers birth certificate and his renunciation document. But he has not released the proof that his US citizenship had been applied for and approved, and a CRBA issued.
That is a very fine point, and post!
Citizenship at birth is automatic.
For example, had no one applied for US citizenship for Cruz, he would have zero proof that he was even eligible for such.
False. No one had to apply for citizenship for Cruz. He had citizenship at birth.
To document his citizenship, his parents could have obtained a U.S. passport or a Report of Birth Abroad of a Citizen of the United States. Either is acceptable and sufficient proof of citizenship under the law, but neither is required. See 22 U.S. Code § 2705 - Documentation of citizenship and 7 FAM 1133.6 Evidence of Claim to U.S. Citizenship Under Sections 301 and 309 INA
To obtain a passport, Cruz or his parents had to meet the requirements under 22 CFR 51.43 - Persons born outside the United States applying for a passport for the first time.
But he has not released the proof that his US citizenship had been applied for and approved, and a CRBA issued.
He likely does not have a CRBA because his parents were not required to get one for him.