I’m not understanding this at all. A simple call by anyone to any NY Board of Elections will tell you who’s on the ballot. If Cruz did or didn’t say this a simple phone call would verify it either way so why say anything?
Cruz thought he’d drop it out there, someone clued him in, and he tinkered with his story to save face. If you followed the Ben Carson thing you’ll see this is his MO.
However, 2 different reporters, from 2 different outlets, reported it exactly the same way... contemporaneously. Only later, is the explanation changed.