When you check your serial number and it's eligible , you have the option of booking an appointment , what the above poster says that apple took a booking to fix the phone, and when they arrived, were told no batteries in stock.
It is apple that should be contacting the customer and saying not to come in if they know they cannot repair it. It costs the customer time and money to go into an Apple Store .
How would you feel if you made a booking to fix your car , and on the day of arrival you were told to comeback as they were out of parts....don't forget it's very very hard to get a convienet time slot in a busy city.
Also they are not offering a free battery cause they care, it's cause they are legally obliged...in most part of the world, and imagine the global uproar when apple is fixing faulty devices only in some countries. They have no choice, it's a manafacturing fault.
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They used to give refurbs, but these days they will replace batteries. Mind you if you really get along with the genius they can probably upgrade you to a refurb

my last 5s with a bad battery got replaced
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They will always give you a credible reason, never will they say they don't have a theory on why something is wrong. Even when support has had not clue how to help me, they have acted like it was in my best interest and they had an answer.