I remember when I was at the Apple store because my 6S would randomly shut down. They also tried to tell me my battery was perfectly fine at 96%. In the end they agreed to replace it thought, because they have a menus on their diagnostics software where they could actually see that I had multiple shut offs at 20% and higher.
My rep refused to let me see the iPad after his test app failed to complete on my wife's iPhone 6s+ 3 times in a row. lol. Just stated: "Sorry, your battery is good. Nothing we can do."
Link to someone else who agrees that Apple will refuse to replace batteries unless it shows it needs it on their end:
Apple is slowing down older iPhones based on battery wear level [MERGED]
I guess you got a better rep than I did