I've checked the classes source and my PiwikTracker object $tracker.
$tracker->ip == $_SERVER['REMOTE_ADDR']
So why would $tracker->doTrackPageView('foo') record with $_SERVER['SERVER_ADDR']?

REMOTE_ADDR is typically set to the client address. if not, it may be you are using proxies or other configuration where IP is set in another header. you can see which IP to use by looking at the output of var_dump($_SERVER);

You seem to have misunderstood.
On my server $_SERVER['REMOTE_ADDR'] is the client IP, just like it should be.
Also the PiwikTracker->ip holds the client IP, just like it should do.
However, when calling PiwikTracker->doTrackPageView() the Server IP is recorded by Piwik instead of the client IP.

I also tinkered with the proxy settings in the Piwik config like your issue resolving readme suggests, nothing changed.

I also used setTokenAuth() and implicitly used setIp() to write the client IP into the PiwikTracker object. On calling doTrackPageView it again recorded the server IP

it should definitely work if you call setTokenAuth and pass a token with admin access to the given website in piwik. If it still does not for you, you can debug the tracking api requests see here: http://developer.piwik.org/api-reference/tracking-api#debugging-the-tracker

I found the issue, I leave this here for future reference.
Your documentation is lacking or I misunderstood/overread something.
Like it said here [1] I did the following:

<?php
  require_once "lib/PiwikTracker/PiwikTracker.php";
  PiwikTracker::$URL="http://foo.bar.com/";
  $tracker = new PiwikTracker(1);
  $tracker->doTrackPageView("foo.dev");
?>

Almost everything worked like intended, $_SERVER['REMOTE_ADDR'] and the PiwikTracker holding the client IP, but Piwik recorded the server IP.

The help on this suggested to find the client IP in your $_SERVER' and send it manually. So I did. The documentation says that setIp()needssetTokenAuth()` thus I tried:

<?php
  require_once "lib/PiwikTracker/PiwikTracker.php";
  PiwikTracker::$URL="http://foo.bar.com/";
  $tracker = new PiwikTracker(1);
  $tracker->setTokenAuth("XxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXx");
  $tracker->setIp($_SERVER['REMOTE_ADDR']);
  $tracker->doTrackPageView("foo.dev");
?>

This resulted again in Piwik recording the server IP. Which is odd, given the next step and solution.

Then I went back to the first code without setTokenAuth() and enabled debugging and saw that Piwik reports that the request lacks the rights to record CID, which equaled the client IP.

So, lastly I did this:

<?php
  require_once "lib/PiwikTracker/PiwikTracker.php";
  PiwikTracker::$URL="http://foo.bar.com/";
  $tracker = new PiwikTracker(1);
  $tracker->setTokenAuth("XxXxXxXxXxXxXxXxXxXxXxXxXxXxXxXx");
  $tracker->doTrackPageView("foo.dev");
?>

This now properly records the client IP in Piwik. Unfortunately the documentation in [1] nowhere states that setTokenAuth() is required for this to work. Alternatively there's a bug that requires regular tracking to have admin rights.

[1] https://piwik.org/docs/tracking-api/#tracking-api-reference

Thanks for the details @mahammer - I've added a call to setTokenAuth in the guide you linked. if you have other suggestions to improve our docs please let us know 👍