Here are the criteria that would determine it is a "log cabin style" v a true log cabin:- Foundation Walls = Concrete Block- Roof Surface = Metal or Shingles- Heating = FWA- Interior Walls = Drywall or Plaster

get more estimates , if they come in the same  , grab a shingle eater  , nail gun and dumpster and do it yourself . 

Their latest property which the flat roof addition of the home has absolutely no pitch (shingled) which made me think of the R905.2.2 Slope section of the IRC.

He also required sheer wall to go all the way to shingles even though city architect approved plans that only had it go to ceiling (also the removed load bearing wall that was removed only went to ceiling).  

As you pointed out with your ac example, which could be a roof if you have shingles, or siding if you don’t have stucco.

I initially paid out of pocket for most of the interior updates / rehab costs when the family moved in, but now it could use new roof shingles (which we've got estimates on) and some minor updates in the kitchen and garage.

I have a strong work ethic and don't shy away from hard physical labor thanks to my granddad making me carry pack of shingles up on roofs at 6am during my summer when I was 11 years old, my pay was dinner that night lol. 

Well........they sent a picture of a section of the roof, some of the shingles are u and guess what- NO insurance on it now.    

Just responded on PM, and the home was built in 1982, and the roof is made of asphalt shingle.

Is market like Texas where they often have soil/foundation issues, or like MN/the Midwest where the asphalt shingles might have hail damage?