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It will probably need more than just a screen replacement. You can take it to Apple and see if they will replace only the screen, but once they open it, if water got into it like you said, then the entire device would need replacing. Apple has nothing to do with insurance, so it is up to your insurance carrier as to what they would do.
the device is safe and works as good as new, just the stains are an issue.
What do you mean it is safe? While it may be working now, it will stop. Water and electronics don't mix, and it will eventually fail. I have already explained what you need to do about the stains, see about the screen replacement. However, don't be surprised if they say the entire device needs replacing. If there is water damage, they will not just replace the screen, since they warranty their work, and won't warranty a phone that has water damage.
Question: How do get rid of the yellow stains left after moisture has left the iphone screen?