For what it's worth I have never had measurable nitrates in any of my low-tech tanks. And I haven't had BGA in any of them either. And I have had other algae types, most notably thread algae and some spot algae. That's just one very unscientific data point though.
On the other hand, this
scientific article might be the counterpoint to my anecdote. I vaguely remember learning in an ecology class once that the N-P ratio plays a major role in determining the dominant algae during blooms in natural lakes and rivers.