Refurbished phone prompts me for previous owner's password
You might have some oddball combination of a serial number that's still enrolled in either Apple's DEP or Apple's Activation lock.

I don't know how to check DEP other than by calling Apple support and explaining your situation and asking them to explicitly check to inform you whether that device is or is not enrolled in DEP. https://www.apple.com/business/dep/ If the device was enrolled, presumably it could be pushing that user's account credentials to your device, but that's a really a remote possibility in my experience.

Some advice:


It's really your insurer's responsibility to deliver you a working phone. Even if they tell you to go to Apple - do that and then go back to the insurance company and ask for a proof of purchase. Apple requires written documentation of the original purchaser to bypass activation lock. If this device is somehow still locked - you might get locked out.
Keep in mind that Apple won't divulge private information about others - so be clear you are not asking them to tell you who purchased or locked or enrolled that device - just that you are uncomfortable using the device with someone else's account in it and you need their help establishing whether it's locked in Apple's records correctly or erroneously.
Get everything in writing and consider writing a letter to the insurance company so you have it documented that you had this issue and tried to resolve it.
Apple refurbished products come with warranty service - so you should be able to also see when that device was purchased by contacting Apple or using this web form - https://selfsolve.apple.com/agreementWarrantyDynamic.do Then ask the insurance people when they purchased it from Apple - the dates should match.




If you wanted to power off the device, you could try wiping it from iTunes or erasing all content one last time, but it seems you already did that and clearly the device is retrieving the account information from Apple's servers during the activation phase. Good Luck and please make an answer here when you figure out what happened or if this was just a bug in Apple's records that got fixed without you needing to do anything.