OP - Heres how it works.
Your insurance should be set up to provide you with refurb replacements thru Sprint at a Sprint store if its still under warranty or out of warranty and they cant fix it, and it does not have physical or liquid damage.
If it does have physical or liquid damage THEN you have to file a claim with Asurion and pay your deductible. Your allowed 2 of them per calendar year. Asurion is the insurance company Sprint and other carriers use for insurance on the devices.
Sprints refurbs should be better quality then Asurion units. Ive seen many units come from Asurion that still had issues.
Apple refurb units should be the best quality as apple is the manufacturer and they go back to themselves for the replacements. I have no problems getting a warranty device / refurb from Apple because they are the manufacturer and its easy for them to refurb devices. In some cases you get a new device because apple is great with its customer are in its apple stores.
So if it were my device, and it was under warranty, id go to apple first. As long as there is no liquid or physical damage, and its in its 1 year manufacturers warranty apple is the way to go.
Outside of warranty with no liquid or physical damage go to a Sprint store and use your insurance to get an in store "advanced exchange" replacement. Those are Sprint refurb devices.
IF its lost, stolen, liquid or physical damage Sprint will require you to file an insurance claim with Asurion and they send you one of thier refurbs.
Remember the insurance company is separate company from Sprint. So the supply of equipment is different.