And all that it does is simply "spider" the site and save the pages to HTML.
You could get the exact same effect using curl or wget, we just use the plugin so that my non-technical employees can effectively click a button, get the zip file, and send it to someone who's got access to do the deployment.
What about using `wget --mirror` (with the set of right command line arguments to adjust it to your needs) on a local dynamic site to obtain a fully functional static copy that you can then upload to any server?
This, and the plugin option suggested by jasongill above, sound like they would suit my needs. I don't mind hosting wordpress to use as an editor (as performance is not important). I just don't want Wordpress to be in charge of serving the content.
For me, I'm afraid that this is not 100% reliable solution for me.