The ultimate arbiter of who is eligible is the council of 50 separate State AG and/or SOS. The governors as the executive authority over those offices in many, but not all, states also are part of the council.
There's about 100 people who ultimately decide who can access their ballot.
If even ONE state declines to allow Cruz ballot access (for any reason, constitutionally valid or not) he would have to sue to the USSC under Original Jurisdiction.
The USSC would then have to decide if that state's reason for keeping him off the ballot was constitutionally valid, again under Original Jurisdiction.
I don't see that anyone but the states have standing.
IMO, the Constitution is still the law of the land and States may not supersede its basic tenants....but is 2016 after all, let's party!!