In Czechia, something called bank ID is commonly used to authenticate. The point is to verify it is you, for example when you sign a contract online, fill in tax returns online... stuff like that. The way it works is that you are on some site, you get redirected to your internet banking, you log in (that's what I meant by "bank details", I am sorry about expressing myself so clumsily), and your bank redirects you back to that site with confirmation that is you.
Do I need to verify my identity when someone wants to send me money? Who knows. This is the part that made me check. But I was close to not checking simply because it is habitual, and you do stuff like that automatically.
Nowadays, we are often dealing with systems we do not fully understand. You get redirected to some familiar login form, you log in, and you don't even pause. Well, at least I do it. I should be a lot more careful, apparently.