Okay, I'm convinced. Mostly because it clearly doesn't work. After a bit of research, the issue is with firstbits.com.
Originally it told me my firstbits were "1slan". But blockchain.info returns a different address for those firstbits:
1sLanGJHUdTBnFgqHUgq2fggx3UaMryvT
So, I entered that address into firstbits.com, and now it says that that address has the firstbits "1slan" and that my address has the firstbits "1sland".
Clearly some very sloppy programming on the part of Firstbits.com. This is not reliable at all.