All phones have the issue with turning off when the CPU load is too high for the battery to handle as the battery ages.
He's referring to the general issues with lithium ion batteries. EOL batteries won't be as stable for voltage, cold weather effects battery performance, low charge reduces available voltage, etc.
Ok, but that isn't at issue here. No one is complaining about the batteries except in relationship to how they were affected with iOS 10 and the respective iPhones. This isn't a issue of just "old batteries."