It could either be his screen, or, if all you did was change the BG color in the properties panel, I reccomend making a new layer called "BG" or "Background", creating a square or something the size of your stage, and then publish and test it.
It's not a browser issue, it's a Mac vs PC color scheme setting issue. They are notoriously not the same. The only way to get them as close as possible is to use Web Safe color numbers.
Another thing to look for is fade settings. A transparency setting of 65% will look like 65% on a PC, but will appear like about 95% on a Mac. Never found a fix for that.
the problem was not that the color was a little off
the problem is that the bg color of the swf and the bg color of the html are slightly different from each other.
i think my solution will be to tile the background with tiny jpg's of the color.
the BG jpg will be produced in flash, so it should match the swf's BG color, no matter what computer it is viewed on.
Here's another option. Publish your movie from the html tab in publish settings. Set the Dimesions dropdown to Percent, 100%. then down lower, set the Scale dropdown to No Scale and publish the html. Now, open the html to edit the source, and add this at the bottom of the head tag;
Your movie will show at the size you made it in the center of the screen and the edges of the background color you set in flash will go all the way to the edge of the browser. You won't need a bg image tile or color at all.