I think the show jumped to a ocean seen for a second there?
They do look like sponges, and there are many fresh water sponges throughout the world. I pulled one out of a water intake from Lake Michigan about the size of a baseball mitt a number of years ago, and they are quite common in the US Great Lakes, although there they are more flat, than forest like.
But in Lake Baikal there are forests of freshwater sponges.
Even in a small lake like Barumbi mbo in Africa there is a cichlid that uses sponges as a primary commponent of its diet, the cichlid is Pungu maclareni
I thought about the freshwater sponges, but for me there are large 3 problems.
The ones from Lake Michigan are cold water sponges (temps in L Michigan average around 50'F.
Another problem is that when threatened, sponges use a kind of chemical warfare to protect themselves, and could easily take out an entire tank if picked at by a fish.
And the other, maybe most important factor, is that the food required to keep them alive might be hard to come by. Some ingest free floating algae, and other planktonic particulate and other microscopic substances that are often not a normal part of our aquarium biotope.
While they might make it temporarily, over time starving to death and fouling the tank, in a similar manner many clams do when placed in home aquariums.
A sponge taken from saltwater will not survive in freshwater, period. They aren't meant to do that. It's like taking a coral and sticking it in freshwater- it'll just die. Also, most sponges die when exposed to air.
Plus, saltwater sponges feed on plankton, and there just isn't that much plankton in freshwater.