As a (former) organic chemist, this is spot-on. "Organic" doesn't really have a strict definition, but it's not so much "majority carbon" as it is presence of a C-H and/or C-C bond. I personally don't consider diamond and graphite organic, but some do. Carbon disulfide and phosgene (COCl2) usually aren't regarded as organic. And as you mentioned, stuff with carbon and lots of carbon atoms is a grey area (looking at you, azidoazide azide, but not looking at it too hard, it might not like that).