i have recently taken over a flash based site for a company that had their in-house designer create and program the site.
here is how the site functions:
• MAIN.swf is loaded into INDEX.html
• when user clicks on a section tabs, SECTION1.swf is loaded into EMPTY_mc inside of MAIN.swf.
The designer's suggestion doesn't seem right to me, but you can try it. When you publish a webpage from Flash, to avoid the 'Click to Activate' problem, Flash generates a file called 'AC_RunActiveContent.js'.
This has to be uploaded alongside any webpage which contains Flash...but the fact that the website currently opens the Main.swf would suggest to me that that is not the problem. You say the site works fine locally, so the problem might be in the publish settings.
In the flash section, there is a drop-down option for local playback security. You can change this to Access Network Only. This is an option I've never had to go near, but might help you out.
http://www.YouTube.com/ShiveringCactus - Free FX for amateur films