Cold stone chimney originally designed for an open fire – fire puts out say 12kw and 9 of those go straight up the chimney, keeping it nice and warm and drawing well.
Put a 5kw stove in there and theres probably only 1.2kw going up the chimney as the stove is so efficient at putting heat out to the room. Chimney runs much colder, slow flue gas, condensation, tars form on the inside of the chimney potentially catching fire. Problem is exacerbated by regularly slumbering the stove.
Much more chance of smoking back into the room aswell.
Fitting without a liner to see how it goes is fine but not presure testing first is a bit silly, both for you and the installer. If it goes pear shaped the buck stops at him.
Stainless liner is fine for a stove but fit decent 904 rather than 316 grade and insulate it. No need for concrete lining.