It is strange that carbide precipitation problems are seldom mentioned in welding literature regarding martensitic stainless steel. Far from being an expert, I can only give you my observations.
Since martensitic stainless steel has only moderate corrosion resistance as compared to austenitic stainless steel, I would imagine that carbide precipitation would not be as important since the environment is not a severe. The most common uses for martensitic stainless are high temperatures, where oxidation and strength are the main concerns, and high hardness applications where moderate corrosion resistance is required. Of course an austenizing heat treatment after welding would improve corrosion resistance if corrosion resistance is important and other stainless steels are not suitable. Also, not all martensitic stainless steels require preheat. Cast Stainless CA6NM, and forged stainless F6NM (much less common) can be welded without preheat. PWHT is recommended though in all but a few cases, and it can be beneficial to heat it up quickly and water quench.
As far as the mechanisms involved, this is a guess, but I think that microstructure has something to do with it. Since austinite has a much higher solubility for carbon than ferrite or martensite, the austenite can retain the carbon in solution to room temperature, then when heated to the sensitization temperatures, the increased mobility of the carbon allows it to diffuse to grain boundaries where it combines with chrome because chromium carbides are a more stable form than free carbon (lower free energy). Martensite on the other hand doesn't want to retain carbon in solution, so if carbides form, it is probably during cooling after transformation from austenite, and the carbides are dispersed thought instead of in one place. So when welding, there would be less free carbon in the matrix available for precipitation, and the carbides that have already formed do not deplete one specific region. Does anyone else know the mechanisms as to carbon reactions in martensitic stainless????
One thing I do know though is that for high temperature martensitic alloys, they sometimes add vanadium and tungsten, which preferentially form carbides over chromium as a strengthening mechanism.