ABM, insurance companies have access to satellite photos of your home. They can measure the slope at your house and then calculate the area based on the satellite photos. It's simple geometry. There's no need to get on your roof if they can see the damage from the ladder. Hopefully your roofer has also included the 10-15% waste that results from putting a new roof on.
In looking back, I think that roof process I followed was telling: when I think I'm right, I'm a huge a-hole. I do the same in this forum.
You are right. Just found out this morning that they've ordered something by the name of Eagleview analysis. Good call.