Image style is not rendering
The answer was simple, $user is the user logged in. As my logged in user didn't have a profile image, all I kept seeing was the default. Unfortunately, elsewhere on the page I am not using $user but just $field_*, so it looked like I was using the right variable. This fixed it:

&lt;?php $account = $elements['#account'];?&gt;


And then updated $user to $account. 

&lt;?php $to_render = field_view_field('user', $account, 'field_image', array('settings' =&gt; array('image_style' =&gt; 'header_image_160x160'))); print render($to_render);?&gt;  


You cannot believe how much time and searching I did to fix this, and it turned out I was looking at the wrong variable the whole time.

Thank you,
Paul.