I have a FileTailerDocument that extends PlainDocument - it spawns a
thread that reads a file, and when the file gets new text in it, it's
inserted into the Document using
 private void insertText(String textToInsert)
 {
   writeLock();
   try
   {
     int insertLen = textToInsert.length();
     int afterSize = this.getLength() + insertLen;
     if (afterSize > bufferSize)
     {
       this.remove(0, afterSize - bufferSize);
     }
     this.insertString(this.getLength(), textToInsert, null);
   }
   catch (BadLocationException ble)
   {
     ble.printStackTrace();
   }
   writeUnlock();
 }

The part of the program written by the other team uses that Document in
their JTextArea, by doing a
   playbackStatusTextArea.setDocument(logController.getTailerDocument());
   playbackStatusTextArea.setEditable(false);
   doc.addDocumentListener(
       new DocumentListener() {
           public void changedUpdate(DocumentEvent e) {
           }
           public void removeUpdate(DocumentEvent e) {
           }
           public void insertUpdate(DocumentEvent e) {
             // On insert, scroll to the bottom
             SwingUtilities.invokeLater(new Runnable() {
               public void run() {
                 playbackStatusTextArea.setCaretPosition(
                   logController.getTailerDocument().getLength());
               }
             });
           }
       });
But when I update the file, they end up scrolling to a few lines before
the bottom.  I've tried printing out the length in the insertUpdate, and
it is the same as the length of the file in bytes.

I've tried this on Mac and Linux, and it's the same result.  (The
writeLock()/writeUnlock() and SwingUtilities.invokeLater() were
unsuccessful attempts to make it work right.)