The information they have is more than just Date of Birth or Baptism date etc.
Those records show things like "sins / judicial reprovals / and elders reviews of one's 'spirituality' etc"
It contains a summary of the person's value if you like. And if the individual is deprived the opportunity to see those records, then that is what is disturbing! A person's character can be maligned in an inaccurate way, and yet they have no right of reply.