Well, sort of. Obviously any time a headline includes speech marks you can normally assume it isn’t true. What has been found, however, is that the branches of birch trees lower by about 10cm over the course of the night.
An open access article in Frontiers in Plant Science explains how researchers in Finland and Austria used lasers to scan trees multiple times through the night. By the time morning had arrived the branches of the two trees studied were, on average, drooping 10cm lower than at the beginning of the night.
If you look at the image below you will see two scans overlaid on one another. The Black dots are from early in the night whilst the red dots are from the next morning. In fairness to them, the branches do seem to have drooped.
We know that the droop is caused by a reduction in the water pressure in the cells of the tree but the key, unanswered question is whether this is an active process guided by a day-night rhythm within the tree, or is it a passive process dictated by the light available in the environment?