Short answer: yes, it is possible.
Longer answer...
HTML, CSS, PHP and MySQL are already many languages, but I guess he means that most major sites have a heterogeneous back-end. This is probably not out of choice though -- more often it is historical. As people change and new technologies emerge, new pieces are built with different languages and frameworks.
I have built a forum and Q&A sites with HTML+CSS+PHP+MySQL and many other people have done the same, so this set of tools is without a doubt adequate for building something like this. In fact, I would argue that you could build almost anything on the web with that combination.
A more interesting question (that will generate more heated response) is what framework you use on top of that. A CMS like Wordpress of Drupal, or an MVC framework like Zend, CakePHP or CodeIgniter.
Or whether you should be dropping PHP entirely and using something like Django or Ruby on Rails. Knowing more than PHP will definitely help you to be ready for newer approaches.