I've never had a chimney fire with the 3 fireplace stove inserts at my house. I do keep a chimfex and other bottle type extinguishers on each level of the house to cover any type fire. I had a SS liner inserted into the chimney which consisted of several sections screwed together and it went directly into the top of the various wood stove fireplace inserts we've had over the last 30 years. AND, a crucial point, the chimney is a prefab unit, and where the flue exited above the roofline on the gable peak, the dual flue outlets, one for oil furnace, one for wood stove, were separate. The furnace had a metalbestos flue, the wood stove insert had the SS, which terminated, and was sealed at the metal top of the chimney stack. The prefab chimney stack was cased in vertical wood planking and the top of the entire unit had a fabricated metal flashing to keep water and wind from getting down the two flues.
Caution if sealing SS pipe at joints with caulk, only use caulk that is fire rated to withstand high temps. It is usually red in color, and is meant to be used for sealing places where a fire could go from one floor to a higher floor via electrical penetrations where there is conduit, etc. Also designed to seal flue sections - see link below; and their website has numerous tabs to select info on other hearth care and solutions.
Also note that sealing the insert stack keeps unwanted cold air out and keeps lethal gases of combustion contained so they can only exit via the top of the insert to atmosphere.
I would definitely also use heavy duty metal pipe tape to further seal any air or gases from escaping the insert where they could leak into the house.
Rutland products:
https://www.rutland.com/p/3/500-degree-f-rtv-high-heat-silicone-sealant
BTW, I would have the stacks checked annually, and I burned hot fires, 850-900 degrees, and had a fire temp gauge in the stack, AND on the stove surface to monitor the situation. The wood stove SS stack/insert NEVER showed any amount of creosote and only ever needed a light brushing with a chimney sweep brush.
Trust me, the extra expense is well worth the added peace of mind for you and your family, friends using your house/cabin. Chimney fires are preventable, so do what makes sence and learn from other's experience. A chimney fire is something that kills way to many people/families when it could have been prevented in most cases.....