Using Flash FLVPlayback component with skin on Facebook (FBML)

Question

I'm trying to insert a player on a Facebook Page tab with FBML with fb:swf. I have the following:

<fb:swf 
  imgsrc="http://IP/player/player.gif" 
  swfsrc="http://IP/player/player.swf" 
  flashvars="source=http://IP/player/movie.flv"
  swfbgcolor="000000"
  wmode="opaque"
  quality="best"
  width="520"
  height="430" />

I can see the video, no problem. It plays inside a FLVPlayback component, which uses a skin (referred by /player/skinName.swf, I tried also the absolute path here). This player works perfectly everywhere else (even on an iframe Facebook application, where it's not inserted using the fb:swf tag, but with object, of course). However, I can't see the skin on the Page tab.

Any ideas?