It is a surprising effect. First time I saw it I was very surprised.
As Bucky says, a stream does hold water. However, there is more to it. It's not just the "settling of water within the rocks". Even if your stream was a smooth chute into the pond, and the water shot fast straight into the pond there would still be some amount of water in the chute, and the amount would stay the same.
This effect also depends on the pump size. When you first turn on the pump you don't instantly see water flowing back into the pond. After a second or so you see water slowly start over the falls, the stream slowly fills and then you see water flow out of the stream and into the pond. That whole time your pump was running full bore pumping water out of the pond. That amount of water stays in the falls/stream. One drop in, one drop out. So the larger the pump the more water will be in the stream because water flows slower thru the stream and volume increases.
Topping up the pond is the fix...but...get ready for your next surprise...after you top the pond off what happens when the pump is turned off? All that water in the stream now comes back into the pond and can overflow the pond. Start up the pump again and you have to top off again. Of course this depends on how close to the actual top you "top off".
One more surprise...evaporation. You will lose water by evaporation in the pond but also in the stream and falls. But the stream and falls will always be topped off by the pump. All evaporation loss will appear in the pond. If your neighbor's pond loses 1" per day your pond might lose 2-3" per day. That leads many people to worry they have a leak.