Yes, Fire has serious problems with Buddy lists, but there's a way around them.

I could not get Remove Buddy to work either, so I used the official AOL IM client to remove the buddies I wanted to. Then when I re-opened Fire, the buddies were back! It turns out that to remove buddies you must exit Fire, use AOL IM to update your Buddy list, then throw away /Library/Application Support/Fire. Now when you relaunch Fire, it won't re-corrupt your Buddy list, though you will have to re-enter all your account information. Having to jump through such hoops is highly annoying, so the developers really should fix this.