I think your fetch array call is fine, and now, it shouldn't be ==, it's right as it is.
This might be the problem.. the line you have is..
$sql = "UPDATE Passwords SET `password`='$encrypted_pswd'";
I would instead try..
$sql = "UPDATE passwords SET password = '" . $encrypted_pswd . "'";
a couple of things here.. your field password had single quotes around it in the sql string, I've never seen that before. Also, when building sql strings, I've had the best luck with concatenating , i.e. string = "something" . $variable . "something else", rather than having the variable inside a double quoted string expression.
Last but not least, you might want to consider some different naming conventions to avoid confusion, and eliminate case as a possible error source.. for example, if you have a table object dealing with passwords, you might use tbl_passwords as a name. The field storing the password might be fld_password. all lowercase, with underscores instead of spaces, and a naming convention for objects and variables can simplify the process.
Ok, I rambled, please give the sql string a shot and let us know if it makes a difference.. best of luck.