What sites should really say, is what dumb "password restrictions" they forced you to use on signup. For example sites should have a message that says:
"We are dumb enough to force your password to have at least one Uppercase/Lowercase/Number/Symbol and it must be at least 8 characters long, but you can't have consecutive numbers, this may make it different from your usual password pattern and force you to recover the password every goddam time you try to use our site".
"We are dumb enough to force your password to have at least one Uppercase/Lowercase/Number/Symbol and it must be at least 8 characters long, but you can't have consecutive numbers, this may make it different from your usual password pattern and force you to recover the password every goddam time you try to use our site".