It's nice to see the positive publicity with Peter, but I think the internet hype over that puzzle is badly overblown.
I think the hype shows a) internet click-hunters are desperate to cash in on "the next big viral thing", and b) a lot of adults are badly out of practice in applying logic systematically. It's entirely appropriate that this problem is presented to bright middle-school students. I suspect even adults who find it bewildering at first blush could be trained in an hour or so to solve this type of problem easily if they were motivated and willing to overcome their "logic is too hard" bias.
As you remarked about yourself, the thing people are missing is a strategy for how to approach this type of problem. Once you have that, it should be pretty straightforward. It has a lot of similarity to "logic grid puzzles", which are commonly found in puzzle books for young people. The "tricky" part is understanding how to set up the grid, and how each statement affects the grid. As in the solution shown by Peter, you can work it out without resorting to a grid, but a grid helps demystify the process of elimination and inference once you understand how to use it.
[url=http://en.wikipedia.org/wiki/Logic_puzzle#Logic_grid_puzzles]http://en.wikipedia.org/wiki/Logic_puzz ... id_puzzles[/url]