It has always been recommended to keep it wet here.

The chemical process of hydration in concrete will occur wether or not it is protected from surface evaporation but keeping it wet will allow the concrete to retain the original mix water and keep it from getting too hot therefore the need for curing is dependent on the air temperature, humidity and wind.

In a hot windy climate protecting it will not only increase its strength and permeability but also decrease the likelihood of cracks which can increase its durability.

But even in a cool humid environment keeping concrete wet can't hurt. You should spray it to avoid marking the surface.

So when a concrete contractor told me not to worry pouring into water-filled forms because the concrete would just displace the water, he was, ah, exaggerating?

If you are pouring walls that are on a concrete footing the water will probably be displaced and no problem...if you are pouring concrete footing/sidewalk/slab in water/mud that is a REALLY bad idea and you can expect the concrete to settle.