That quote really hurts. My iPhone 6S has had spontaneous shutdowns since the first winter it was out (and is supposedly not in the replacement program). No previous Apple phones did. This winter it's the same. To me it suggests a more widespread defect that they do not wish to admit.
So got my battery replaced today because of this thread. Feels very smooth again but may be between my ears. Only now realize I forgot to do a benchmark test with the old battery still in.
Had the same problem - they told me I‘d have to wait up to 8 weeks for them to return my phone. I instead chose to pay a local repair shop €50 to swap the battery within 30 minutes. For €80 they would have used an original Apple battery replacement.