It's hard to say which companies do what and for what reasons. Here in the northeast, wood fired heat is a fact of life. I have never heard of deterioration of a chimney because it was used for venting a wood fire.
Most carriers in Northern New England will underwrite risks (homes) with wood supplemental heat. Many will not do it if the wood heat is the primary heat, both for the fear of fire as well as freeze-up if the occupants are unexpetedly taken away from the house and the fire goes out. A good rule of thumb is less than 50% of heat generated from wood.
Generally, companies require risks to meet NFPA 211 standards, which dictate things like clearances of wood appliances to combustible construction, as well as regulating distance from the chimney to wood framing (2 inch airspace), etc. They also dictate that a chimney flue can only vent one type of appliance. For example, you can't vent a wood stove and an oil boiler into the same flue.
As far as insurance on property in more rural or remote locations, all companies use a system where they rate what is called protection (fire) class. They rank from PC 1 through PC 10. Properties with fire hydrants close to a full time fire department have a low protection class number. Risks more than 5 miles from the fire department, especially with all volunteer squads and no available water source are higher protection class. It's simple math and common sense. Remote property with volunteer firemen and no water source tend to burn flat. Volunteer firemen are wonderful, often well trained people, but by the time the fire is discovered, dispatched, they get out of bed and get to the firehouse, start the trucks, drive 5 to 10 miles, it's too late. This is opposed to full time, fully trained firefighters, a mile or two from the station with a pressurized inexaustable supply of water. Those properties rarely burn flat. If you were a company, which house would you choose?