Hm, are you sure they didn't say "we don't cover battery
degradation under the battery warranty"? Because they definitely cover battery issues under the battery warranty, but it's pretty clear they don't cover battery degradation for Model S/X. I'm not even sure how they could even make such a statement before they've even looked at the vehicle though.
Really it just comes down to whether or not Tesla finds an issue with your battery. If there is something wrong, you should be covered under the battery warranty. If they find nothing wrong, they are not obligated to replace anything. Unfortunately battery degradation is a grey area because what defines "wrong" in terms of battery degradation? A sudden decrease in capacity, definitely. A slow degradation like you've been experiencing, although faster than the "average", is a grey area because it depends on so many variables. A person living in a cooler climate that charges to ~70%, always leaves it plugged in, has a fairly short commute, is going to have a much different experience with battery degradation compared to someone who lives in a hot climate, charges to 100% frequently and leaves it there, doesn't keep it plugged in, and has larger depths of charge. I'm not saying you're doing either, just trying to illustrate it's hard to make a comparison. You really need to pull the total capacity off the CAN bus to know how much battery degradation you've experienced. Using displayed range is not an accurate way to estimate. As for the car shutting down at 16 miles, absolutely abnormal but doesn't necessarily mean something is wrong with the battery (although there is a good chance something could be wrong).
All that to say, I'd be very surprised if Tesla is trying to pull a fast one on you and trying to save the company $20k (or however much a battery replacement cost). Even with my absolutely terrible experience dealing with their customer service, I guess I still have faith in the fact they'll honor their warranty. Please do let us know what the end result is as I'm curious to find out what their assessment is of your battery and what they choose to do about it. Best of luck!
Edit: Here's a
post I made showing an example of how big the difference can be between displayed range versus the actual total capacity (kWh) for comparing battery degradation.