On my phone interview with an US company in 1999, they asked me what salary I wanted. I told them "in my previous remote job, I was making $3.25 an hour; I would like $4". They replied "we'll give you $6". (Romania, Eastern Europe - this was about 8 times the average salary.)
This was the only time someone offered me more than I was asking :)
I've been on the hiring end of similar conversations. Often the thought process is that you're dealing with salaries so small compared to what they're used to that it's worth quite a bit extra to get someone who is so happy with what they're paid that you increase retention and don't have to spend time hiring replacements as often.
It can be one of the great parts of negotiating with someone located in a much higher paid location.
This was the only time someone offered me more than I was asking :)