I find that hard to believe. Grasslands that are managed in the suggested way become nutrient poor and support way less life than a naturally grown forest. Everybody is eating from trees: nuts, fruit, leaves even the wood itself.
A natural forest - not the managed ones with just a couple of species - is absolutely teeming with life.
However, there is something in between nutritionally poor wildflower grassland and thick dense forest and I feel those hit the sweet spot.
Finally, I feel biodiversity is often given so much value that we don't even think about the amount of life anymore. It turns out that some ecologically managed grasslands do have a high number of species, but just not a lot of each one, whereas an open forest can harbor way more animals.
This makes sense: there is just not a lot to eat when you only have wildflowers on the menu.