A bit more on this. The code in FCKEditor was somewhat mixed up, and just getting FF to convince it that it was IE did not appear to be an option.
Then I checked out all the free editors mentioned here:
http://www.geektips.net/119/best-free-wysiwyg-html-editor.html
All of them did exactly the same thing with the exception of TinyMCE, which also did it, but only in FireFoxe's "view source" not their own "view source", which was interesting, so I did some further investigation. I might have some of this wrong, it is all new to me, so don't get antsy if there is an incorrect observation, just be nice and point it out.
When FireFox (and all browsers I suppose) download and interpret a web page, they scan through the Document Object Model and compute internally how to present that page. These are known as computed styles, rather than 'inline styles'.
Now, when FCKEditor or any of the other editors above, besides TinyMCE switches to Source / HTML view, what it gets back from FF is the computed styles, not the original styles.
It would appear, that when accessing the DOM via javascript in the "standard" manner, whatever that might be, IE will return the original style attributes, but FF returns the computed style attributes, and this is why the original style attributes get lost in FF in these editors.
An interesting tool that helped in this investigation is the DOM inspector for FireFox described here:
http://www.clagnut.com/blog/340/
It was using this that I found out about computed styles, and found that it was the computed styles that were going through to the text editors via javascript requests from FF.