DIY fix for iPhone 5 sleep-wake button issue
Apple's warranties are world wide however you may give up walk-in service by some authorized repair centers if they don't want to take that repair. You can arrange service in the US (since your original purchase was from the US) over the web or by phone. The mail in procedure is clearly explained at https://ssl.apple.com/support/iphone5-sleepwakebutton/

I've never heard of actual Apple stores not offering to help facilitate a US repair - even if it's helping you arrange a mail in service, but perhaps something new is up or it's a temporary delay due to parts shortage.

That being said, there's nothing preventing you from opening up the device and putting in a new sleep/wake button. For some, that "surgery" is way too hard for their skill level with tools and for others, it's a "piece of cake" since they are either trained or have the natural aptitude for repair of delicate electronics. If your device has the covered issue, it is caused by a mechanical failure and/or electrical failure of the switch itself.