I have not yet read the women's charter, but I do not see anything wrong with MCYS making it easier for marriage records to be accessed. Afterall there is a limitation as to how much and how frequently one person can access.
I know of at least one acquaintance who was duped by her boyfriend, when he was actually married. He led a double life. I think this acts as a safeguard to innocent parties out there, and as a deterrent to would-be cheats.
Your colleague sounds mighty childish to resort to such threats. And being divorced once before isn't anything to be ashamed about. Anyway nobody knows the reason and you are not required to tell them the real reason.
I don't know what exactly it is to fear, but I don't see why you would really need to explain to your company in depth if the time comes for it. No lies, ok lah.