Ok so just for kicks I choose no editor just to see if that changes anything. I did just as you said to edit html in a custom html module which worked perfectly fine (it works fine with an editor too). I then added the bold tags as seen here:
It strips out the bold tags but not the text. hmmmmmm.... and yes I even tested my template with this:
<p>text to display</p>
The text worked perfectly without being stripped out. So does news show pro allow you to add custom html in the field shown in the picture above? Have you tested it? (I don't mean this statement to sound rude in any way)