One of my daughters doesn't buy anything that Apple is saying about the battery being the issue (i.e. "....because older batteries could otherwise periodically overload"). She had an older iPhone5 with a swelling battery that caused the screen to push out. Apple said "That's our problem." She was offered a brand new iPhone5 for $100, so she bought one.
Her brand new iPhone5, purchased earlier this year and which would presumably have a brand new battery, has slowed right down.
