To restate the question:

I own the example.com domain title. My actual webhost (thanks to a buddy) is a few.website.org.

I would like individuals to have the ability to visit example.com and find out some.site.com/example/. The truth is, I only want the URL bar to exhibit example.com/whateverpage.html.

I have been studying and experimentation with mod_rewrite, but can't quite decipher it. Is whatsoever possible?

You could just host a fundamental web site by having an iframe. How complicated may be the site? Who provides your dns - sometimes there is a web sending setting for this purpose.

And are you certain you cannot just alter the domain title on the website you're tugging from?

You'll need a CNAME record inside your DNS that aliases some.site.com as example.com.

http://en.wikipedia.org/wiki/CNAME_record

If you and your friend don't get access to, or don't understand how to customize the DNS server... Contact the Host Company that's hosting the website, they ought to know how to create DNS CNAME records properly. The wiki above includes a couple of good examples of the items a CNAME record appears like.