What They Saw
They looked at different kinds and amounts of fixed nitrogen and their effect and different gases in the atmosphere. Many experiments used ammonium phosphate or other forms of ammonium, and they thought maybe the drop in pH seen as ammonium was consumed led to decreased hydrogenase activity, but actually even when they used forms that didn't allow a pH drop, they still saw the same decrease, suggesting that it's the fixed nitrogen itself that leads to decreased activity. Which makes sense.
They found, consistent across species, that ammonium led to the biggest activity decrease, about 60-80%; nitrate as little as 20%; and glutamate hardly at all. I think these cultures were not adapted to these compounds though.
So they tried adapted cultures too. They found that the more fixed nitrogen they added, the less hydrogenase activity they saw. Adaptation didn't matter with ammonium, but cultures adapted to nitrate had more of a decrease in activity. Apparently they didn't test glutamate.
Then they compared cells with various nitrogen sources grown in air or in a hydrogen-oxygen mixture. They didn't test cells without a nitrogen source in this gas mixture though, maybe because they couldn't grow. Anyway, the hydrogenase was always more active in air with no fixed nitrogen than with any kind of fixed nitrogen (as seen before), and with H2-O2 the activity seemed even lower, even than with the same fixed nitrogen source in air. Activity was almost zero in nitrate-adapted cells given nitrate. This seems odd; previous studies seemed to show that hydrogen stimulated hydrogenase activity.
What This Means
I'd say other studies showing stimulation by hydrogen were more convincing, but at least this one was consistent showing an adaptation effect and down-regulation in the presence of fixed nitrogen.