Answer: Yes it can!
I recently received a wall post from my brother saying something like: “Check out this hot new site I found…” followed by a short link, which led me to what looked like a facebook (FB) page asking for my password. Without even thinking, I typed in my password and hit enter. Then I immediately realized what I had done so I went to my FB profile and changed my password. I then contacted my brother who reported it to FB and changed his password.
Apparently, a friend of my brother’s appeared to have posted a note (she was hacked too) on his wall leading to what looked like a FB page asking for his login and/or password. He thought it was legit. Next thing you know, it looked like he was posting on everyone else’s wall asking his friends to check out a certain business or “on-line” opportunity. Some links asked for a FB login while other lead you to some get-rich-quick scheme.
Important: As long as you are already logged into FB, you will never be asked for a login or password except when you want to make changes in your profile, like your password.
The fake wall post may say something like “Here’s the best facebook apps in my opinion…” with a web link to a site asking you for your username password or to some kind of ad about making lots of money. Once they get your login information, they will then begin using your friends list to post the same information on their walls.
Hope this helps. As far as I know, FB now has a good handle on it. The key thing to know is, once your are logged into FB, they will never ask you for your login again unless your changing your password yourself. If you have any questions, you can contact FB from there help link or perhaps I can help you.
Have fun but be safe!