Regarding statement freshness, derefr already answered. Regarding username/password, in Brazil at least yes (sort of) - you log in with account number and a password, but it's sort of a "read-only password" - you can see statements and stuff with it, but if you want to actually move the money, a different password is required.

Trivia: this is used by a Mint-like company in Brazil called GuiaBolso - you give them just the "read-only password".