<p>Per this <a href="http://kb.adobe.com/selfservice/viewContent.do?externalId=608abffd" rel="nofollow noreferrer">Adobe KB tech note</a> is there any way around having to place the FLVPlayback skin SWF in same directory as HTML file the container SWF is loaded from?  It pains me to have to put a SWF in my site's root directory.</p>

<p>I think loading the Flash video in an iframe would solve this problem, but is that a good practice?  I generally shy away from using iframes because of padding, margin, and sizing issues between browsers.  Maybe that's not an issue anymore with CSS.</p>

Well, you can place the skin in another directory as long as you specify the path (relative to the loading HTML) in the "skin" parameter for your FLV playback component in the component inspector. Troubleshooting is very easy if you use the Net panel in Firebug or a similar tool.
Using an iframe works and don't cause rendering problems as long as you take care that there's no margin or padding inside the iframe. However, you will need another HTML file which can make maintaining your site more of a hassle.
If you are publishing a lot of video files, you might find that it's more convenient to use a standalone player such as the
JW Media Player
.