Seems like a nesting issue to me lol... I think that if a ubbcode is used inside another codebox that neither should show, as neither are properly nested.
I think it should show as
====================================
[b]This is a test of a quote using the bold UBB Code, which extends into two words within the quote itself:
[quote]
This is bolded.[/b] This isn't bolded.[/quote]
If this is a bug, then the quote box will not function properly as a result of the way the UBB Code was used in making those words appear in bold print.[/quote]
Since nothing is nested, nothing should be parsed, in my humble opinion anyway...