What tyranny? They're a hidden society that seems to specialize in organizational paralysis. It's unclear they could dominate the local coffee shop even if the MC's father was around to break ties.
I don't think you're entitled to someone's secrets just because you're dating them, especially not secrets that could literally get people killed. As ThorinKing said, the ring is symbolic because marriage is generally considered the most significant commitment you can make to another person; that's the point at which all your cards should be on the table (even if a few of them have to be kept face down for security purposes).
Kaija and the MC weren't even officially dating, so I don't find it surprising she didn't spill the beans on the hidden world to the MC. That's a life-changing revelation if ever there was one. If their relationship had continued to deepen then I agree there would come a point where she'd have to confess the full truth, but they weren't there yet. From what the game shows, it's unclear whether they would ever have gotten there had fate not intervened.
IMHO, the only truth Kaija absolutely owed the MC at the start of the game was to be honest about her feelings for him. Unfortunately, her honesty on that crucial matter is retroactively governed by
our choices, which makes it very complicated to assess
her blame in a consistent manner.