Online answer sites are appealing to many people. A couple of reasons for this appeal are probably the anonymity of asking a question when no one can know that it's you and the ease of just typing in whatever you are thinking. The questions I saw on the various sites were about a plethora of topics such as whether it's okay to lie to an employer and one about how to brush a dog's teeth.
I think these questions should be directed to a library if people will actually ask some of these questions at a library. Some of the questions may be strange or considered inappropriate even but it doesn't hurt to answer them at the library. I don't think any question should be outright ignored. For example someone called the library one night when I was working multiple times he wanted to know how to spell the name of a certain kind of marijuana because apparently, at least this is what he said anyway, he wanted to know how to spell it for a tattoo he was getting.
People most likely know about the library but then choose these answer sites because they are easy to get to and more accessible from home.
The slam the board events and what they do does look interesting and will educate people more about where answers are coming from. Another aspect of this is seeing the nature of the answer boards, anyone could still pretend to be a professional or librarian if they really wanted to. Overall though it's an interesting idea/might teach people something they need to know.
Online answer sites are going to always be used because they are anonymous and easy to use but knowing about them and encouraging patrons to ask questions could raise the visibilty of good information and that the library is here to help.