Thanks for such a nice concise explanation. That's exactly what I needed. It's that kind of explanation that I'm looking for with the WebAssist instructions.
However, the curious thing is that I did your fix with changing the code on mail_PHP.php. And then it worked. (Meaning the emails were showing up with the proper CSS formatting.)
Then after that, I did the updating the Server behavior fix. And it now my emails are coming in with text only again!
After updating the mail_PHP.php file with your fix - it works again. So my comment here would be that the fix from the official WebAssist update appears to be buggy. (Because it replaces the mail_PHP.php file every time I update the server behavior when I'm tweeking the design and layout of the email.)