would this test depend also on the fungal flora? fungi don't care if carbon is in cardboard, wood, corn cob, or underwear form.

Whether that is worthwhile would depend on how long the "test" took. If the Soil Food Web consumed the briefs in a week or took several months would tell you something, but knowing that you had adequate amounts of organic matter in the soil to feed the Soil Food Web should be of more value.
A lot of researchers are coming to the realization that soils need organic matter, something organic growers have known for well over a hundred years.

I too think there are a lot of potential variables at work here. Not that it doesn't correlate to soil health in some way, but unless they did a controlled study comparing the results to conventional soil test results as well as crop yield, how would you know? In fact I would have guessed that the more active soil would have degraded the cotton faster, not slower. But what do I know. :-]

I know one thing: some of those pundits who make fun of gummint funded research studies would have a field day with this one! Literally. I can see some people really getting their knickers in a bunch over this. OK, I'll stop now.