The program has worked this way for many versions.
The one thing I failed to mention is the 'support folder' (it's been a while since this topic came up again)
You must remove the MP3 from this folder.

Example;
If you save your web designer file as mysite.web then the program will create a folder named mywebsite_web_files
This is the store for the assets used for your site and which is drawn from when published.
If you open this folder (it will be in the same location your save the mysite.web to) and remove the *.MP3, it will not longer be published and the problem is solved.