That statement could mean a number of things. For example, it could mean that your insurance company would cover you under your existing policy, as long as you made a timely report of the purchase; or it could mean that under your loan contract your lender would not deem you to be in breach of contract as long as you obtained full coverage within 24 hours.
Does the finance manager recall making the statement? If so, what is his explanation of what he meant?
The dealership knew that you had the minimum level of insurance required by law. I'm not aware of anything that would require them to ensure that you obtained any additional insurance, even if your loan contract required you to purchase additional insurance.Quoting DanM
There's an enormous difference between stating something and implying something. When you rely on inference, you substantially increase the chance of a misunderstanding or miscommunication.Quoting DanM
If you heard this from your lawyer, who has fully reviewed the contracts and facts of the case, then it's reasonable to work with your lawyer to try to resolve the matter. If you heard this from your buddy, your neighbor, a random stranger... as would appear to be the case... it isn't a helpful analysis.Quoting DanM
The biggest problem with seeking rescission, even if we assume a basis for rescission, is that when the contract is unwound the parties are to be restored inasmuch as possible to their original position. You can't do that without repairing the car.
If you can clarify what the manager said, and what he admits to having said (ideally in writing, to limit later denials), that could be helpful in analyzing a potential legal claim.

