Hi Bob,
This is interesting, the code you have there looks right and usually if you have the age set to 13+ it's not a problem. One thing, did you add the Javascript to your page? I'm assuming you used this page: http://developers.facebook.com/docs/reference/plugins/like-box/ to create the box right? And selected the HTML5 option? If so, then also make sure the correct JavaScript was added right beneath the tag.
I did a little searching as well and found this post on stackoverflow that might help http://stackoverflow.com/questions/7268100/facebook-likebox-showing-fine-but-only-if-logged - although it sounds like you're doing it right.
Hopefully this helps!
Jen
Maybe they're trying to compete with the Pinterest button. 
And Thanks to everyone for being so helpful!