Your statement is misleading. That website is essentially creating a hashed password of the original password. But the target website will still consider it your password in which case it will not protect you once the 'password' to the website is known which the author is talking about.
To put it another way, if your password is 'abc' and hashed it becomes: 'ABCDEFG'. The website stores it plaintext as 'ABCDEFG' to which a hacker has it. Then if anyone later accesses the website, they would be able to just type in 'ABCDEFG'.
Pwdhash is just another form of a password manager.