That's not what it means, and I don't think any large number of people actually think that's what it means. It means the account is verified to be owned by X,
I beg to differ. Twitter accounts of individuals come across as a personal medium, not a mass propaganda outfit. I would be extremely surprised if a majority of users realized that an individual account with a blue checkmark was actually being run by a team.
As for sharing passwords: Twitter has to have mechanisms for detecting multiple logins to the same account.