Apologies for the length of this post.
I don't think either are lying. As a self prescribed battery hobbyist, I must admit I'm not entirely sure what is going on. I have watched all of my devices with coconutBattery since the 6+, to the 6s+, to the 8+, and now Xs MAX. I take weekly readings and focus on the battery capacity vs design capacity. I usually keep my phones for 1.5-2 years. My wife gets the same phone I do so I have 2 phones to "observe" and compare against with very different usage. I'm a light user and my wife is a heavy user of her phone.
After 2 years and 230 - 300 cycles my phones have had little to no battery degradation in terms of overall capacity. The worst was my 6+ that went from 108% from design capacity to 98% after almost 2 years. Most of my other phones strayed a percentage or two (6+ and 8+) - this includes iPads.
My wife's 6s+ was the only anomaly in our lineup of phones from the 6+ to the Xs MAX. She had a bad battery from the factory. Less than 6 months into ownership, her phone would randomly shut off and last easily half as long as my identical phone. coconutBattery showed her battery capacity randomly fluctuating between 40%, 60%, and 90%. Of course, when we took it into Apple, they showed "green" and healthy. We showed them how it shut off below 70% with any load. They shrugged their shoulders and had to be forced to let me pay them for a new battery out of pocket. In so doing, they destroyed my wife's 6s+ and we got a new 6s+. Later on, during the battery fiasco that spawned the Battery Health reader in iOS, Apple refunded us $50 without us having to do anything.
Batteries are a chemistry. Getting an accurate reading on them is difficult, especially over time. Battery capacity can vary depending on when you do the reading. For consistency I only read at full charge. I've seen a 3-6% capacity difference when reading below a full charge, even more at a 20-40% charge. On an older battery, this capacity difference will widen significantly, especially if a reading is taken further away from a full charge.
Apple's health meter is definitely pre-programmed to take a different approach to reading battery capacity. The fact that your phone's performance management was enabled means the battery dipped below acceptable voltage. This is the same thing my wife's 6s+ did (voltage drop). I believe Apple got a batch of bad batteries that had difficulty maintaining their voltage as the phones aged hence their willingness to do cheap battery replacements to help satisfy these unhappy customers.
I do not see a problem with a phone having a 95% capacity after 1000 cycles. My boss' 4s had 86% capacity after many years and 1200?+ cycles. Battery wear is not linear like a glass of water. It is not a guaranteed thing that after 500 cycles your phone's battery will be 80% capacity - Apple just warranties that it will be >=80%.
I don't think coconutBattery is inaccurate. I do think reading a chemical reaction like a Lithium Polymer battery is "difficult" and not 100% accurate after time. I think that these batteries dip in voltage and capacity from 20-60% and tend to stabilize more after 80% charge when doing capacity readings.
On the topic of Apple's Battery Health meter - I think they only read at near full charge and probably are programmed to read high values because if it showed 80% or lower it would qualify the user for a replacement on a less than year old (or two for AppleCare+) phone.
This is only my opinion - I'm a battery hobbyist only. My only claim to fame is that I've read
https://www.amazon.com/Batteries-Portable-World-Rechargeable-Non-Engineers/dp/0968211844/ several times. The author of this book is the author of
https://batteryuniversity.com and I've had the privilege of conversing with him via a short email.
[doublepost=1553223411][/doublepost]I wish companies would give us more access to battery information. I imagine companies prefer to keep this information "hidden" as it would show non-favorable results.
My Dell XPS 15, purchased last year (2018) during Black Friday, according to Window's own battery report, has lost 10,000 mAh since I bought it. My Samsung Note 3, rooted, showed it losing 50% of its design capacity in less than 7 months (thankfully batteries were easy to replace and cheap). My Dell D830's battery couldn't hold a charge after a year and shut the laptop off instantly when unplugged.
One reason why I prefer Apple products is that they, in general, have had far superior battery life and longevity over other products I've had in the past.