You could, however, advertise that short link to users and set up a 301 redirect so that when people request that URL they are redirected to the real location of the content. With a 301 redirect, there would not be a Duplicate Content issue.
Would it just be easier to put the index.php file on the top level domain, (put it in www.example.com/copyofwiki/ and point the index.php paths to the subdomain wiki files? Then since I only want "one" page...the root page from the wiki basically, I can 301 the whole folder to the top level domain.
You don't want to 301 links that people click on on the pages of your site.
I don't understand what you mean by "301 the whole folder to the top level domain". You need to think about both "URLs the user sees" out on the web, and "internal paths to real files" inside the server.
They are two different things that are only 'associated' but NOT equivalent.
If you change URLs you need to redirect old URLs to new URLs.
You also need to rewrite URL requests to internal server file paths, adjusting to suit.