Well a Consular Report of Birth Abroad is the function equivalent of a USA Birth Certificate. So without one Cruz has no claim to US citizenship. I recently lost my picture ID, I had to go thru hell to prove I was a US citizen and get a new picture ID and new SS card. I need certified medical records to get the SS card, then I needed my Birth Certificate, SS card, bank statement and two recent bills showing my address to get the ID card. But as we found out yesterday laws and rules are for little people. Not elites like Ted Cruz and Hillary Clinton whom Cruz and all the other #NeverTrump ers appears to be supporting over Trump.
A CRBA doesn't change one's status. It merely confirms it.