I'm only speaking for Verizon experiences here and asurion. I cant find anywhere on asurion where I can start my own insurance with a phone bought thru swappa or third party, it says to add it thru your carrier. I know Verizon will not let you add it unless within a certain day amount after buying it thru them, used to be 15 days. Verizon does offer open enrollment once a year, but you have to wait for that to be offered. There are other options like square trade, I don't know how those work, I do know I seen one that specifically says they cover ebay phones, you have to send receipts in and other processes and coverage does not start till it's all complete. I think that is what Mike Dee is saying, it's more difficult to insure phones bought third party with good reason.
I do know I ran across this with Verizon, it's been awhile ago, but the refused to warranty a phone less then a year old because I bought it thru a third party like ebay, Swappa. It was not bought thru my Verizon account thru Verizon, best buy, sam's club,Samsung direct, authorized agent and so on. They said since I bought used from a private seller they don't do the warranty, I would have to go directly thru manufacturer for warranty.