Is there a way to link to the middle of someone else's page even if they don't have an anchor?

Yes you can. If the person has an element with an ID anywhere on the page. For example:

<div id="someId"></div>

Then you can create a link to this page like:

<a href="http://somePage.com#someId">Middle!</a>

The only thing you need to do is choose an Id in the middle.