Earlier quoted context omitted.
I tried to find more information about this statement: "When authenticating the login you authorize one of Klarnas third parties to log into your bank account as you, allowing them to pull records of all your financial transactions, account statements etc.“ Do you have any source to verify this claim? That they can and do pull down this information. I would like to know if they really have all that information or not…
I don't know if they do have it, but it is absolutely possible after the login. I saw it reported in an IT-security facebook group and made my own purchase from a site that use them (gottebiten.se), paying directly from bank account. The login was indeed done by a Klarna 3rd party using my ID number, and not from my device. You have to confirm once more for the payment to be sent.
I just paid using their direct payment method two times the last week or so. Will be more on the lookout in the future and try to keep an eye on these things.