What you could try doing is editing the Main Index Template (index.php) by replacing the theme-specific code with the "normal" Wordpress code that most themes use -- the code that pulls a certain number of the most recent posts, regardless of category. I don't have this particular theme, so I can't see how it works, but I have the feeling that it may be difficult to tweak because it has its own control panel, where you can adjust different settings. There's probably some code somewhere in the theme that looks for the settings that you have selected, and you might start getting PHP error messages if you remove some of the code.
If I'm understanding you correctly, you'd like the blog to show a certain number (like 10?) of posts on the home page, and you want them to be the most recent posts without consideration as to which categories they belong. If that's the case, then it sounds like you're more interested in the design of this "Our Magazine" theme than you are in its functionality (e.g., the slider and tabbed content area shown in the demo). Is that true?