It's contradictory at all. There's no mechanism by which adding nitrate directly reduces nitrate. As I said in my post, it's possible that something is nitrate limited and adding nitrates will give it the nutrients it needs to grow. But that's far from a guarantee.
It's not smart to assume that dosing nitrates will reduce phosphates because there's no direct mechanism or pathway to do that. If you'd like to claim that in a lot of cases it does, you're probably right and I don't take issue with that. But we should not be telling people that dosing nitrates will reduce phosphates because it just doesn't.
In every tank I've ever dosed nitrates into (that had zero detectable nitrates) phosphate always decreased rapidly. I've done at least 30 tanks that were low nitrate and needed to start dosing. I think its safe to say that dosing nitrates will likely reduce phosphate (indirectly) and it would be a very good idea to have some on hand. It would be very bad advice to tell people that dosing nitrates will have no effect on your phosphate levels because it most certainly will and it doesnt hurt to have phosphate on hand and a phos checker to be prepared.