My 3 year old cannot open the fridge, she doesn't have the strength/dexterity. She cannot open lids either. She cannot fix any kind of meal without making a mess. With play-doh she pretends to make meals and definitely makes a mess (and enjoys herself tremendously in the process).

She absolutely cannot go to the supermarket to buy anything, and she cannot cross the street either.

A 3 year old doing all those things... I'm willing to believe some can, but it's definitely not the norm, and not because we don't let them. They just can't.