You might want to check with a couple other title companies to see how they would handle it based on the language in your contract of sale. If they would do the same thing that is what it is although to me a buyer's policy is a buyer's policy and a lender's policy is a lender's policy. Also it seems to me that just about everything is handled a little differently in The Villages.
Practices vary from state to state but except in Sarasota County in Florida the seller customarily chooses the title company and pays for the buyer's title policy.
Not that is is likely to be a concern for the OP but title insurance companies do go out of business every once in a while. I owned several commercial properties in Albuquerque, NM when the title insurance company I had used to close became an issue to my lender, not the bank mentioned in this article, but another. The bank holding my mortgages insisted I reinsure every single property with a new policy which I did. It was unexpected and expensive but necessary. Big whoop! I got the reissue rate.
Title Insurers''' Low Reserves Stir Worry - The New York Times