They are accountable, that comes with having the power. But they don't have to run a person who is not qualified. They wouldn't run with a 30 year old, for example.
The person who is denied the opportunity can seek relief in court on some civil law claim, breach of promise or something like that. The party holds the door open for all who are qualified, I meet, the party rejected me.
Plus there is accountability in the public eye. Do you want the party to front unqualified candidates? How about an unqualified nominee?
Cruz can be knocked out easily on constitutional grounds. There is ample case law precedent on the subject, and the RNC has lawyers. Trump can't be knocked out on constitutional grounds.
Would not the RNC be liable for allowing an unqualified person to run and certifying eligibility if he was NOT eleigible? . McConnell has refused to declare Cruz eligible like congress did McCain. That should be grounds enough for the party to act and seek declarative judgment IMO