Of title insurance is that you are insuring yourself on past claims on the house (Leins, collateral), I could be wrong but that doesn't apply to your debt owed on the house and is obtained at time of purchase of the house. Again this is my limited understanding but the provider of this insurance checks your title for any Leins. They can't find it so they are willing to insure. Feeling that there research was good enough to be right on this bet. I can't see why somone would insure you knowing you owed money or had Leins outing your house.
Somebody please let me know if my understanding is wrong.