Scientifically, their position seems to be this, and it is falsifiable: Any closed and sealed ecology (like Bios-3, or Biosphere 2), comprised of a limited selection of species, and cycling in isolation from the general ecosphere, will die.
This premise seems to be at the bottom of concerns about loss of biodiversity, extinction of species, loss of habitat and loss of natural capital (or ecological services). The fear seems to be that even the loss of a few species can severely disturb the web of life, and perhaps even lead to the extinction of mankind. And that is why maintaining biodiversity is so important.
But is the premise true? Here are my thoughts:
1) There is life at hydrothermal vents on the sea floor, feeding on hydrogen sulfide, which does not even need the sun. These colonies appear to be self-sufficient, and making no draw off the ecological services of other species. Therefore, it is possible to live without services from the general ecosystem. Similarly, we might find self-sufficient life on other planets, like Mars.
2) "There have been many attempts to construct small, closed ecosystems. For example, Clare Folsome sealed small aquatic ecosystems consisting of algae, brine shrimp, and other organisms in glass flasks (Folsome and Hanson 1986). Although the flasks were prepared in the 1950s, some of them still retain fuctioning mini-communities (Nelson et al. 1993)."
http://www.aibs.org/bioscience/bioscien ... ext.html#1
3) Previous mass extinctions have not caused the extinction of life itself. Therefore, even verterbrates can survive despite wholesale destruction of ecological services.
4) It's really hard to kill versatile, omnivorous animals by depriving them of ecological services. How much of the environment would you have to kill in order to exterminate all rats?