Is it correct to directly modify a supplied Drupal theme?
No, it's not correct to directly modify a contrib theme (or Drupal core, or a contrib module). Once you start doing that, you cannot easily update the theme anymore. It a few months, you, or another, developers may forget the theme was modified, do what should be a easy update and break everything.

You have two options to change and existing theme. You can rename the theme before making any other change (ie. fork the theme to a custom theme). You can also create a sub-theme of your chosen theme. The sub-theme can override template and theme functions, and adds ins own process and pre-process functions. But it will inherit all non-overridden templates and theme functions and all process and pre-process functions.