phpbb is a very secure, reliable and extremely popular forum type. It has no known vulnerabilities, and if any are detected, they are usually 0-day. Many global companies use phpbb. I can say without a shadow of a doubt that phpbb was not the cause of the problem.
The more likely cause was that you re-used passwords. If I use the same passwords everywhere, and one of those sites gets hacked, then I can reverse MD5 your password from the hacked database. Bingo, I can login everywhere you used that password. This is what happens to most people.
The second most likely cause is that you downloaded like the world is ending tomorrow, disregarding any safety precautions and clicking on .exe files as if you were on a slot machine. One or more of those .exe files contains a keylogger or cookie reader. This is the second most likely cause for being hacked.
Lastly, the third most likely cause for being hacked is disregarding the importance of folder permissions. Uploading a forum, ignoring which folders to chmod and which folders to move out of public_html.