And the answer is...
When you bind a Dashcode Text part to a datasource there is a popup menu that comes up to choose what type of binding is created. One of the choices in that popup menu is "HTML".
If you select "HTML" when making the binding the text part will render the html embedded in the bound text data.
When I originally set up the binding I had selected "Text" from that popup menu. This caused the text part to display the text "as is" without rendering any embedded tags.
I kept looking for a place in the program to change that setting (once I found out about it) and it appears now that you have to reestablish the binding in order to invoke that popup menu. There does not seem to be any other way to edit the setting.
I'm just really relieved to find out that this works. I hope this helps someone else who gets stuck as I did.
Cheers!