Yes Fixing the Hut gives skills but Examining the Hut Does not give skills. If you pay attention to a villager when their working, after their done examining the huts it just switches to "nothing" with no message at the bottom, but fixing switched to "nothing" with the " this villager has gained skills" message. so if you see a villager examining pick em up and drop em till it says fixing, certain sides and angles of buildings will give you one or the other.