I am a fellow noob who was puzzled by this too. The answer is actually fairly simple. You need to used the fb:else tag.
<fb:visible-to-connection>
<fb:else>
</fb:visible-to-connection>
Now, according to the facebook docs, you need to use </fb:else> as well. However, I didn't use that in my example.
This is what I did, and I know it works because I include screenprints in the example:
facebookanswers.co.uk/?p=83
However, the closing else may be needed to make it "proper", so its worth trying it with them in first. If it doesn't work, just remove them as I did.