Happened to me at an airport in Thailand. Some airside police officer demanded to inspect my passport, then wouldn't give it back to me until I walked him to an ATM so I could pay him a "tax" in cash.

I never went back to Thailand.

It most certainly can be done--I wore mine basically 24/7 for a year. The only time it wasn't under my clothing was for border crossing or bathing--and in the latter case it almost always was under a traveling companion's clothing. No close calls--but someone else in the group wasn't so cautious and hers was snatched. Fortunately, the thief wasn't sophisticated, kept the cash and dumped everything else quickly.