I am an analyst for a large insurance company...
You need to actually read some of your policy fine print, and make sure your company (not just your agent) knows your car has a salvage title. Having misrepresented an application, even accidentally (your agent forgot to ask the title status maybe?) can result in denied/very painful claims regardless.
It is true this may vary by state as Insurance guidelines are state regulated, but you want to be very, very sure about this considering the potential financial impact of getting nothing/next-to-nothing for a totalled car.
Banks are at more risk than Insurers, because if they loan you the money to buy one, they are already out that money. If they loan you XX,XXX dollars for a car, they want to make sure that if you stop paying, they can sieze the car and recoup approximately XX,XXX dollars, rather than 1/4 of that because it's a salvage car that they can't find a repo buyer for.
I'm just saying, better safe than sorry. If you can't afford to walk away from it empty handed, don't buy it.