OK. I guess I read something wrong, because I thought any of the three elements you listed would cause a situation to be labeled an accident. And then that last and it's made it look like any of those three elements would make any accident become a recordable. So therefore I didn't see how an accident could be non-recordable.
You have to look at who is defining an accident. This is a somewhat similar situation in what is a CMV. The FMCSA says for the purpose of logging a CMV is defined as over 10,001. A CMV for the purposes of a CDL is 26,001, get my point? This is what you are running into here. The FMCSA basically defines an accident as anything that requires an entry to be made in that carrier's accident register. Carriers and insurance companies have different definitions to the fact some even call them incidents and then further in-house incidents and otherwise. @brian991219 might have something else to add, but that is the way I have always understood was the primary difference between recordable and non-recordable!