Thanks for the password

Here's one for you, do you think Google has too much integrity to try your password on other sites log in as you and data mine personal info from other sites? How about this, what if you enter the password for another site by accident into Google and it fails do you think they would store that failed attempt and try to log in to other sites as you using those credentials? Lately it seems to me if I can imagine it someone is doing it. What do you think?