You won't get a new one no matter how you insist. Like you, I'm not a big fan of refurbished electronics. While the argument can be made that a refurbished unit has been "looked over", the only defining thing that someone can say about a refurbished unit is that it passes certain test. Those are the same tests that they undergo before leaving the factory. My problem with refurbished is why they failed in the first place to then become refurbished.
So I'd be less than happy like yourself in the same situation although it is what it is when it comes to Apple.
Apple won't give you a new phone because it would be against their business model.
Your water damaged phone will get inspected and repaired and will become a replacement unit. If Apple kept giving out new phones, their AppleCare+ business model wouldn't work.
There is one exception to this rule that I've seen very rarely and that is a documented paper trail of replacements that have all failed.
A friend of mine got his girlfriend an iPhone 5c when they launched. It was defective.
Six replacements later (all defective in some way) and having been in continued contact with an AC+ supervisor, the 5c was replaced with a brand new iPhone 5s.
So, it is possible, but you have to have to be suffering major documented problems to get there.
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So Apple decided to give me a replacement iPhone for my liquid damaged XS Max as the Face ID stopped working and they said it wasn’t repairable. However, they told me that I have to use one of my AC+ accidental damage deductible for it (for which I have no problem) but I’m not comfortable with the fact that I will be getting a refurbished unit, even though they denied and said it’s new, but it definitely isn’t as it comes in plain white packaging.
Upon insisting, do you think Apple will agree to give me an actual new iPhone? I do not want any accessories, just the phone.
Apple refers to them as remanufactured.
New casing, new battery. All parts tested, the entire phone tested when reassembled.