This is a very common con in North America as well, and just recently someone tried it on my grandmother, claiming to be me and saying he/I had gotten into a car accident and needed $3000 sent by Western Union right away. It went exactly the way you describe, right down to explaining that the reason his voice sounded different was that he was upset from being in the accident.
She was confused, and told him/me to call my parents, and the con gave up. She told my parents that somehow the con had known my name; as I explained to them, he had certainly gotten my name through a cold read (e.g. waiting for her to say it) and then acted as if she’d said it. They’re very, very good.
Maurer’s classic - and enternally recommendable - book The Big Con from 1940 has, unsurprisingly, some insights on the matter.
He claims that it’s a typical ploy to flatter the mark about their honesty. The con artist can thereby lull them into a form of self-deception: of course they are being honest in entering into this deal because, after all, they are always honest. This is to be encouraged. After all, if they think of themselves as honest, then they wouldn’t enter into a dodgy transaction. Therefore this deal is straight.
While he references the “you can’t cheat an honest man” idea as standard con lore up-front in the book’s opening pages, it’s striking that once he gets down to the details what he emphasises is the notion among cons that good marks are fundamentally liars. They’re the sort who big up the money they have available, the influence they have, etc. When this tips over into active self-delusion, they become very takeable.
There is one type of con (I think it’s a con…) that works best on honest/decent people, actually. I was reminded of it when I saw a trailer for the movie “Choke.” In it, the narrator says that if you can get someone to save your life, you can to send you money for years (I’ve heard that mentioned other places, as well.) The idea being you pretend to choke on food, or almost get hit by a car, and a while after you get the mark’s name and address (to send them flowers and a card,) you start sending them sob stories of your life, and how if you just had a little money, you can get by.