When a title insurer used the phrase "insure over" that means they will NOT place an exception for the item in the title insurance policy.
For instance, let's say there is an unsatisfied mortgage on title that is 60 years old. A title insurer would likely decide to simply insure over the mortgage rather than pursue satisfaction.
So, "insure over" means there is a problem but the problem isn't a very high risk and so the title insurer decides to take the risk of providing coverage even though they have knowledge of a flaw on title.
This concept helps you to understand the difference between marketable title and perfect title. If title insurers where trying to perfect title, they would fix all problems no matter how small. That's not what we do. We can "insure over" items that cause minimal risk and therefore insure marketable title, not perfect title.