Even the official charging hub goes into a wall socket. It all depends on the adapter used. Oddly enough, even 2 adapters with supposedly the same output can differ, so the difference isn't that simple. It probably also has to do with the continuity of the output and other such things (the listed output is generally a max, but not always reached continously. That's why some adapters will charge laptops better than others despite being marketed as the same output). I find Sony products rather picky anyways, my headphones also refuse certain adapters (and I tested 3 different ones).

We don't have gamestop where I live. Nedgame or Used Products has them somewhat regularily. There are also some smaller lokal retrogaming stores througout the country, which are generally the nicests.

But I don't think any of them check this thorough to see if they're real or fake. They filter out the obvious B-brands but the better fakes generally fall trough. It's always best to go in person and check it yourself. And like said, even then it can be hard to determine at times as even official ones can be rather inconsistent.