I was handling all my own meals except dinner and had a house key at around the same age in the US. I'm not sure how drastically things have changed in the ensuing 20 years, but I still see kids walking and playing without adults, so I suspect it's both exaggerated and regional or class-based.
That said, I'm curious as to what age this care would be required? Back In My Day ™ I was entrusted with a house key at a relatively young age (10? 11? it was a while ago...) and would walk myself home / prepare food / generally take care of myself until an adult came home. But these days you hear about police being called for kids playing without an adult present in a fenced-in front yard (and the fact that as I understand the USA is far less walkable than where I live) which makes me wonder what age is considered suitable over there?