I feel like this is easy but I am missing something...
Using jQuery, I am trying to fetch a remote page (on a different server), capture the HTML contents, and inject
You can't do that - the Same Origin Policy prevents it for security reasons (as you've found).
You need to run a proxy script on your own server that your JavaScript uses to fetch the content from the remote server on its behalf.
AJAX disallows cross-domain fetching. You must have your server fetch from whatever server you want to get information from.
If you want to go cross site, you can't pull in an entire page. There is a way to get data from cross domain sites using JSONP. What you do, is make the js call the data you get back as a function which will evaluate json data. But wont work if you are trying to fetch an entire page, however.
Alternatively you could use already-existing APIs like YQL or Pipes to access the data you're after... and then return results using JSONP (cross-domain operable).