It's definitely not ALL containers in the entire game. As almabrds mentioned there's a reason the devs invented the sneak skill, although in some of these cases you have to actually use the steal skill as well. Having said that, increasing those skills seems to make bugger all difference to your success rates.

However, I'm just playing through it again for the first time in ages (also with latest RP) and there are many, MANY places you can steal from that you'd think people would have a problem with. You can practically loot any house in Gecko with the occupants right in front of you and they don't care. In Vault City they're a little bit more uptight about that kind of thing though...

Seems to me that the devs implemented this mechanic for some parts of the game and didn't get around to those other many containers due to time constraints (and the RP never added them either). Which is a shame, as it feels almost like cheating to rob people blind while they just stand there and stare at you.

"Hey, who the hell are you? Oh you're opening all my drawers and checking all my shelves? Oh OK then - take whatever you need!"