First off, I live in Ubon Ratchathani where we have one authorized Apple repair shop.

I went to that repair shop to have the battery of an iPhone 5s replaced. With her limited English, she was saying they don't or can't replace the battery for a 5s. They can however offer a trade program, where I give in the 5s and receive a "new" 5s....total cost 12,000 Baht. Obviously completely unacceptable. I was trying to find out if they just don't have it in stock right now and she confirmed again they can not replace the battery for the 5s. She said iPhone 5 yes....iPhone 6 yes, but not 5s.

That sounds really odd. Can anybody offer any clarity on this?

She wasn't trying to scam, I've been there before with no problems.

I know I can get an aftermarket battery for the 5s at any mobile phone shop, but I would like to avoid that since I've had a couple of bad experiences with after market batteries.

Something wrong here. Maybe they just don't happen to have 5s batteries in stock? You could try calling Apple Support to get some guidance and let them know: 001-800-65-6957

Genuine replacement battery: https://www.appleipodparts.com/iphone-5s-genuine-new-replacement-battery-p/san17.htm