M.P.
I noticed this recently. I think it's new. The ability to share is not what caused the "cat walk disaster." Mamapedia staff posted the question on the Mamapedia Facebook page.
When I clicked on "Share" I was shown icons for sharing. They included gmail, twitter, facebook, and several more. I clicked on the envelope icon and sent my answer to myself. The Gmail gave me the address to the question. Clicking on the address only allowed me to see this one question. It did not give me access to Mamapedia.
I like that option because sometimes a question fits with my daughter's interests. I can send the question to her. What appeared is the question and answers as they appear on the site.
I know many are concerned about privacy. I'm not because I know anything I put on the Internet is not private. Also, the only people I actually know on this site are those with whom I've directly communicated. Why would anyone not a member know who posted especially when they use a screen name or a wrong location.
I suggest that you try sharing to see how this works.
I looked at questions in 2011 and they had the share option. Perhaps mamapedia added it to previous questions when they added the option recently? I only recently noticed it.