They said I would need to drop off the computer with them; they would order a new battery and I could have it back in a week or so. I said I couldn’t do without the computer and I couldn’t let them access the hard drive (not encrypted) as I have proprietary data on it.
They said I could make the full payment and bring it in when the replacement battery arrives, leave it with them and collect it in a few hours. They insisted they could not replace it with me present and the minimum time I would need to leave it was 3 hours. This is easily enough time to clone the hard disk, which I did point out, politely, but they said this was the most they could do for me.
I ended up buying a third-party battery and changing it myself. It took less than 10 minutes. If it doesn’t last long, I’ll just have to buy a new Mac.
So yes, apparently there are no standards in place for data security as far as authorized service centres are concerned.